Enlaces
Aquí podrá encontrar las publicaciones de los miembros del grupo durante los últimos años. |
Title: Realization problems for limit cycles of planar polynomial vector fields. Authors: Juan Margalef-Bentabol, Daniel Peralta-Salas. Journal-ref: ournal of Differential Equations 260, 3844 (2016). Abstract: We show that for any finite configuration of closed curves Γ⊂ℝ^{2}, one can construct an explicit planar polynomial vector field that realizes Γ, up to homeomorphism, as the set of its limit cycles with prescribed periods, multiplicities and stabilities. The only obstruction given on this data is the obvious compatibility relation between the stabilities and the parity of the multiplicities. The constructed vector fields are Darboux integrable and admit a polynomial inverse integrating factor. |
Title: Thermalization of particle detectors: The Unruh effect and its reverse. Authors: Luis J. Garay, Eduardo Martin-Martinez, Jose de Ramon. Journal-ref: Physical Review D 94, 104048 (2016). Abstract: We study the Anti-Unruh effect in general stationary scenarios. We find that, for accelerated trajectories, a particle detector coupled to a KMS state of a quantum field can cool down (click less often) as the KMS temperature increases. Remarkably, this is so even when the detector is switched on adiabatically for infinitely long times. We also show that the Anti-Unruh effect is characteristic of accelerated detectors, and cannot appear for inertially moving detectors (e.g., in a thermal bath). |
Title: Hybrid Models in Loop Quantum Cosmology. Authors: Beatriz Elizaga Navascués, Mercedes Martín-Benito, Guillermo A. Mena Marugán. Journal-ref: International Journal of Modern Physics D 25, 1642007 (2016). Abstract: In the framework of Loop Quantum Cosmology, inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a splitting of the phase space in a homogeneous sector, formed by global, zero-modes, and an inhomogeneous sector, formed by the remaining, infinite number of modes, that describe the local degrees of freedom. Then, the hybrid quantization is attained by adopting a loop representation for the homogeneous gravitational sector, while a Fock representation is used for the inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is expected to provide a suitable quantum theory in regimes where the main quantum effects of the geometry are those affecting the zero-modes, while the inhomogeneities, still being quantum, can be treated in a more conventional way. This hybrid strategy was first proposed for the simplest cosmological midisuperspaces: the Gowdy models, and it has been later applied to the case of cosmological perturbations. This paper reviews the construction and main applications of hybrid Loop Quantum Cosmology. |
Title: Unique Fock quantization of a massive fermion field in a cosmological scenario. Authors: Jerónimo Cortez, Beatriz Elizaga Navascués, Mercedes Martín-Benito, Guillermo A. Mena Marugán, José M. Velhinho. Journal-ref: Physical Review D 93, 084053 (2016). Abstract: It is well known that the Fock quantization of field theories in general spacetimes suffers from an infinite ambiguity, owing to the inequivalent possibilities in the selection of a representation of the canonical commutation or anticommutation relations, but also owing to the freedom in the choice of variables to describe the field among all those related by linear time-dependent transformations, including the dependence through functions of the background. In this work we remove this ambiguity (up to unitary equivalence) in the case of a massive Dirac free field propagating in a spacetime with homogeneous and isotropic spatial sections of spherical topology. Two physically reasonable conditions are imposed in order to arrive to this result: (a) The invariance of the vacuum under the spatial isometries of the background, and (b) the unitary implementability of the dynamical evolution that dictates the Dirac equation. We characterize the Fock quantizations with a non trivial fermion dynamics that satisfy these two conditions. Then, we provide a complete proof of the unitary equivalence of the representations in this class under very mild requirements on the time variation of the background, once a criterion to discern between particles and antiparticles has been set. |
Title: Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics. Authors: Jerónimo Cortez, Beatriz Elizaga Navascués, Mercedes Martín-Benito, Guillermo A. Mena Marugán, Javier Olmedo, José M. Velhinho. Journal-ref: Physical Review D 94, 105019 (2016). Abstract: The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invariance under the spatial Killing symmetries, unitarity of the dynamics selects a unique Fock representation for the canonical commutation relations, up to unitary equivalence. In this work, we generalize these results to anisotropic spacetimes with shear, which are therefore not conformally symmetric, by considering the case of a free scalar field in a Bianchi I cosmology. |
Title: Quantum corrections to the Mukhanov-Sasaki equations. Authors: Laura Castelló Gomar, Mercedes Martín-Benito, Guillermo A. Mena Marugán. Journal-ref: Physical Review D 93, 104025 (2016). Abstract: Recently, a lot of attention has been paid to the modifications of the power spectrum of primordial fluctuations caused by quantum cosmology effects. The origin of these modifications are corrections to the Mukhanov-Sasaki equations that govern the propagation of the primeval cosmological perturbations. The specific form of these corrections depends on a series of details of the quantization approach and of the prescription followed to implement it. Generally, nonetheless, the complexity of the theoretical quantum formulation is simplified in practice appealing to a semiclassical or effective approximation, in order to perform concrete numerical computations. In this work, we introduce technical tools and design a procedure to deal with these quantum corrections beyond the most direct approximations employed so far in the literature. In particular, by introducing an interaction picture, we extract the quantum dynamics of the homogeneous geometry in absence of scalar field potential and inhomogeneities, dynamics that has been intensively studied and that can be integrated. The rest of our analysis focuses on the interaction evolution, putting forward methods to cope with it. The ultimate aim is to develop treatments that increase our ability to discriminate between the predictions of different quantization proposals for cosmological perturbations. |
Title: Cosmic Microwave Background and Inflation in Multi-Fractional Spacetimes. Authors: Gianluca Calcagni, Sachiko Kuroyanagi, Shinji Tsujikawa. Journal-ref: Journal of Cosmology and Astroparticle Physics 1608, 039 (2016). Abstract: We use FIRAS and Planck 2015 data to place observational bounds on inflationary scenarios in multi-fractional spacetimes with q-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints from the tensor-to-scalar ratio, model-independent best fits of the black-body and scalar spectra yield upper limits on the free parameters of the multi-fractal measure of the theory. When the measure describing the fractal spacetime geometry is non-oscillating, information on the CMB black-body spectrum places constraints on the theory independent from but weaker than those obtained from the Standard Model, astrophysical gravitational waves and gamma-ray bursts (GRBs). When log oscillations are included and the measure describes a discrete fractal spacetime at microscopic scales, we obtain the first observational constraints on the amplitudes of such oscillations and find, in general, strong constraints on the multi-scale geometry and on the dimension of space. These results complete the scan and reduction of the parameter space of the theory. Black-body bounds are obtained also for the theory with weighted derivatives. |
Title: ABC of multi-fractal spacetimes and fractional sea turtles. Authors: Gianluca Calcagni. Journal-ref: European Physical Journal C 76, 181 (2016). Abstract: We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. |
Title: Standard Model in multiscale theories and observational constraints. Authors: Gianluca Calcagni, Giuseppe Nardelli, David Rodríguez-Fernández. Journal-ref: Physical Review D 94, 045018 (2016). Abstract: We construct and analyze the Standard Model of electroweak and strong interactions in multiscale spacetimes with (i) weighted derivatives and (ii) q-derivatives. Both theories can be formulated in two different frames, called fractional and integer picture. By definition, the fractional picture is where physical predictions should be made. (i) In the theory with weighted derivatives, it is shown that gauge invariance and the requirement of having constant masses in all reference frames make the Standard Model in the integer picture indistinguishable from the ordinary one. Experiments involving only weak and strong forces are insensitive to a change of spacetime dimensionality also in the fractional picture, and only the electromagnetic and gravitational sectors can break the degeneracy. For the simplest multiscale measures with only one characteristic time, length and energy scale t∗, ℓ∗ and E∗, we compute the Lamb shift in the hydrogen atom and constrain the multiscale correction to the ordinary result, getting the absolute upper bound t∗< 10−23s. For the natural choice α0=1/2 of the fractional exponent in the measure, this bound is strengthened to t∗< 10−29s, corresponding to ℓ∗< 10−20m and E∗>28TeV. Stronger bounds are obtained from the measurement of the fine-structure constant. (ii) In the theory with q-derivatives, considering the muon decay rate and the Lamb shift in light atoms, we obtain the independent absolute upper bounds t∗< 10−13s and E∗>35MeV. For α0=1/2, the Lamb shift alone yields t∗< 10−27s, ℓ∗< 10−19m and E∗>450GeV. |
Title: Particle-physics constraints on multifractal spacetimes. Authors: Gianluca Calcagni, Giuseppe Nardelli, David Rodríguez-Fernández. Journal-ref: Physical Review D 93, 025005 (2016). Abstract: We study electroweak interactions in the multiscale theory with q-derivatives, a framework where spacetime has the typical features of a multifractal. In the simplest case with only one characteristic time, length and energy scale t∗, ℓ∗, and E∗, we consider (i) the muon decay rate and (ii) the Lamb shift in the hydrogen atom, and constrain the corrections to the ordinary results. We obtain the independent absolute upper bounds (i) t∗<10−13s and (ii) E∗>35MeV. Under some mild theoretical assumptions, the Lamb shift alone yields the even tighter ranges t∗<10−27s, ℓ∗<10−19m, and E∗>450GeV. To date, these are the first robust constraints on the scales at which the multifractal features of the geometry can become important in a physical process. |
Title: Quantum spectral dimension in quantum field theory. Authors: Gianluca Calcagni, Leonardo Modesto, Giuseppe Nardelli. Journal-ref: International Journal of Modern Physics D 25, 1650058 (2016). Abstract: We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension ds of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension D. In particular, in the presence of higher momentum powers it changes with the scale, dropping from D in the infrared (IR) to a value d^{UV}s≤D in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value d^{UV}s=2 for any dimension D. |
Title: Timelike information broadcasting in cosmology. Authors: Ana Blasco, Luis J. Garay, Mercedes Martin-Benito, Eduardo Martin-Martinez. Journal-ref: Physical Review D 93, 024055 (2016). Abstract: We study the transmission of information and correlations through quantum fields in cosmological backgrounds. With this aim, we make use of quantum information tools to quantify the classical and quantum correlations induced by a quantum massless scalar field in two particle detectors, one located in the early universe (Alice's) and the other located at a later time (Bob's). In particular, we focus on two phenomena: a) the consequences on the transmission of information of the violations of the strong Huygens principle for quantum fields, and b) the analysis of the field vacuum correlations via correlation harvesting from Alice to Bob. We will study a standard cosmological model first and then assess whether these results also hold if we use other than the general relativistic dynamics. As a particular example, we will study the transmission of information through the Big Bounce, that replaces the Big Bang, in the effective dynamics of Loop Quantum Cosmology. |
Title: Where does the physics of extreme gravitational collapse reside? Authors: Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay. Journal-ref: Universe 2, 7 (2016). Abstract: The gravitational collapse of massive stars serves to manifest the most severe deviations of general relativity with respect to Newtonian gravity: the formation of horizons and spacetime singularities. Both features have proven to be catalysts of deep physical developments, especially when combined with the principles of quantum mechanics. Nonetheless, it is seldom remarked that it is hardly possible to combine all these developments into a unified theoretical model, while maintaining reasonable prospects for the independent experimental corroboration of its different parts. In this paper we review the current theoretical understanding of the physics of gravitational collapse in order to highlight this tension, stating the position that the standard view on evaporating black holes stands for. This serves as the motivation for the discussion of a recent proposal that offers the opposite perspective, represented by a set of geometries that regularize the classical singular behavior and present modifications of the near-horizon Schwarzschild geometry as the result of the propagation of non-perturbative ultraviolet effects originated in regions of high curvature. We present an extensive exploration of the necessary steps on the explicit construction of these geometries, and discuss how this proposal could change our present understanding of astrophysical black holes and even offer the possibility of detecting genuine ultraviolet effects on future gravitational wave experiments. |
Title: Black holes turn white fast, otherwise stay black: no half measures. Authors: Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay. Journal-ref: Journal of High Energy Physics 1601, 157 (2016). Abstract: Recently, various authors have proposed that the first ultraviolet effect on the gravitational collapse of massive stars to black holes is the transition between a black-hole geometry and a white-hole geometry, though their proposals are radically different in terms of their physical interpretation and characteristic time scales [1,2]. Several decades ago, it was shown by Eardley that white holes are highly unstable to the accretion of small amounts of matter, being rapidly turned into black holes [3]. Studying the crossing of null shells on geometries describing the black-hole to white-hole transition, we obtain the conditions for the instability to develop in terms of the parameters of these geometries. We conclude that transitions with long characteristic time scales are pathologically unstable: occasional perturbations away from the perfect vacuum around these compact objects, even if being imperceptibly small, suffocate the white hole explosion. On the other hand, geometries with short characteristic time scales are shown to be robust against perturbations, so that the corresponding processes could take place in real astrophysical scenarios. This motivates a conjecture about the transition amplitudes of different decay channels for black holes in a suitable ultraviolet completion of general relativity. |
Title: From physical symmetries to emergent gauge symmetries. Authors: Carlos Barceló, Raúl Carballo-Rubio, Francesco Di Filippo, Luis J. Garay. Journal-ref: Journal of High Energy Physics 10, 084 (2016). Abstract: Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed. |
Title: Hamiltonian dynamics of the parametrized electromagnetic field. Authors: J. Fernando Barbero, Juan Margalef-Bentabol, Eduardo J. S. Villaseñor. Journal-ref: Classical and Quantum Gravity 33, 125030 (2016). Abstract: We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies. |
Title: Hamiltonian description of the parametrized scalar field in bounded spatial regions. Authors: J. Fernando Barbero, Juan Margalef-Bentabol, Eduardo J. S. Villaseñor. Journal-ref: Classical and Quantum Gravity 33, 105002 (2016). Abstract: We study the Hamiltonian formulation for a parametrized scalar field in a regular bounded spatial region subject to Dirichlet, Neumann and Robin boundary conditions. We generalize the work carried out by a number of authors on parametrized field systems to the interesting case where spatial boundaries are present. The configuration space of our models contains both smooth scalar fields defined on the spatial manifold and spacelike embeddings from the spatial manifold to a target spacetime endowed with a fixed Lorentzian background metric. We pay particular attention to the geometry of the infinite dimensional manifold of embeddings and the description of the relevant geometric objects: the symplectic form on the primary constraint submanifold and the Hamiltonian vector fields defined on it. |
Title: A tensorial description of particle perception in black-hole physics. Authors: Luis C. Barbado, Carlos Barceló, Luis J. Garay, Gil Jannes. Journal-ref: Physical Review D 94, 064004 (2016). Abstract: In quantum field theory in curved backgrounds, one typically distinguishes between objective, tensorial, quantities such as the Renormalized Stress-Energy Tensor (RSET) and subjective, non-tensorial, quantities such as Bogoliubov coefficients which encode perception effects associated with the specific trajectory of a detector. In this work we propose a way to treat both objective and subjective notions on an equal tensorial footing. For that purpose, we define a new tensor which we will call the Perception Renormalized Stress-Energy Tensor (PeRSET). The PeRSET is defined as the subtraction of the RSET corresponding to two different vacuum states. Based on this tensor we can define perceived energy densities and fluxes. The PeRSET helps to have a more organized and systematic understanding of various results in the literature regarding quantum field theory in black hole spacetimes. We illustrate the physics encoded in this tensor by working out various examples of special relevance. |
Title: Hawking versus Unruh effects, or the difficulty of slowly crossing a black hole horizon. Authors: Luis C. Barbado, Carlos Barceló, Luis J. Garay, Gil Jannes. Journal-ref: Journal of High Energy Physics 10, 161 (2016). Abstract: When analyzing the perception of Hawking radiation by different observers, the Hawking effect becomes mixed with the Unruh effect. The separation of both effects is not always clear in the literature. Here we propose an inconsistency-free interpretation of what constitutes a Hawking effect and what an Unruh effect. An appropriate interpretation is important in order to elucidate what sort of effects a detector might experience depending on its trajectory and the state of the quantum field. Under simplifying assumptions we introduce an analytic formula that separates these two effects. Armed with the previous interpretation we argue that for a free-falling detector to cross the horizon without experiencing high-energy effects, it is necessary that the horizon crossing is not attempted at low velocities. |
Title: What gravity waves are telling about quantum spacetime. Authors: Michele Arzano, Gianluca Calcagni. Journal-ref: Physical Review D 93, 124065 (2016). Abstract: We discuss various modified dispersion relations motivated by quantum gravity which might affect the propagation of the recently observed gravitational-wave signal of the event GW150914. We find that the bounds set by the data on the characteristic quantum-gravity mass scale M are too weak to constrain these scenarios and, in general, much weaker than the expected M>104eV for a correction to the dispersion relation linear in 1/M. We illustrate this issue by giving lower bounds on M, plus an upper bound coming from constraints on the size of a quantum ergosphere. We also show that a phenomenological dispersion relation ω2=k2(1+αkn/Mn) is compatible with observations and, at the same time, has a phenomenologically viable mass M>10TeV only in the quite restrictive range 0 < n < 0.68. Remarkably, this is the domain of multiscale spacetimes but not of known quantum-gravity models. |
Title: Do transient white holes have a place in Nature? Authors: Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay, Gil Jannes. Journal-ref: Journal of Physics: Conference Series 600, 012033 (2015). Abstract: The white-hole sector of Kruskal's solution is almost never used in physical applications. However, it can provide a radically different take on the gravitational collapse process, avoiding the problems appearing within the standard paradigm. In this contribution we will try to draw attention to some bouncing geometries that make a democratic usage of the black and white sectors of Kruskal's solution. We will argue that this type of behaviour could be perfectly natural in some approaches to the next physical level beyond classical General Relativity. |
Date: 2015
Subject: Cosmological constant
Comments: Proceedings article
Title: Absence of Cosmological Constant Problem in Special Relativistic Field Theory of Gravity: One-Loop Renormalization Group. Authors: Raúl Carballo-Rubio, Carlos Barceló, Luis J. Garay. Journal-ref: Journal of Physics: Conference Series 600, 012032 (2015). Abstract: There exists a nonlinear theory of gravity which is not structurally equivalent to general relativity and that, in the non-interacting limit, describes a free massless particle with helicity ±2. We have recently shown that this theory can be understood as the result of self-coupling, in complete parallelism to the well-known case of general relativity. This special relativistic field theory of gravity exhibits a decoupling of vacuum zero-point energies of matter and passes all the known experimental tests in gravitation. It is explicitly demonstrated that there is no flow of the effective cosmological constant under the action of the renormalization group at one-loop level, while simple symmetry arguments show that this would continue to be true for higher-loop corrections. The important lesson is that just mild local assumptions concerning the nature of the particle mediating the gravitational interactions are enough to motivate theories which are free of the cosmological constant problem. |
Title: Unitary evolution and uniqueness of the Fock representation of Dirac fields in cosmological spacetimes. Authors: Jerónimo Cortez, Beatriz Elizaga Navascués, Mercedes Martín-Benito, Guillermo A. Mena Marugán, José M. Velhinho. Journal-ref: Phys. Rev. D 92, 105013 (2015) . Abstract: We present a privileged Fock quantization of a massive Dirac field in a closed Friedmann-Robertson-Walker cosmology, partially selected by the criteria of invariance of the vacuum under the symmetries of the field equations, and unitary implementation of the dynamics. When quantizing free scalar fields in homogeneous and isotropic spacetimes with compact spatial sections, these criteria have been shown to pick out a unique Fock representation (up to unitary equivalence). Here, we employ the same criteria for fermion fields and explore whether that uniqueness result can be extended to the case of the Fock quantization of fermions. For the massive Dirac field, we start by introducing a specific choice of the complex structure that determines the Fock representation. Such structure is invariant under the symmetries of the equations of motion. We then prove that the corresponding representation of the canonical anticommutation relations admits a unitary implementation of the dynamics. Moreover, we construct a rather general class of representations that satisfy the above criteria, and we demonstrate that they are all unitarily equivalent to our previous choice. The complex structures in this class are restricted only by certain conditions on their asymptotic behavior for modes in the ultraviolet sector of the Dirac operator. We finally show that, if one assumes that these asymptotic conditions are in fact trivial once our criteria are fulfilled, then the time-dependent scaling in the definition of the fermionic annihilation and creation-like variables is essentially unique. |
Title: Quantum unitary dynamics in cosmological spacetimes. Authors: Jerónimo Cortez, Guillermo A. Mena Marugán, José M. Velhinho. Journal-ref: Ann. Phys. 363 (2015) 36-47 . Abstract: We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent. |
Title: Gauge invariance in simple mechanical systems. Authors: J. Fernando Barbero G., Jorge Prieto, Eduardo J. S. Villaseñor. Journal-ref: Eur. J. Phys. 36, 055005 (2015) . Abstract: This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or graduate students in theoretical physics to understand, in a familiar context, some concepts relevant to the study of classical and quantum field theories. We use a geometric approach to derive the Hamiltonian formulation for the model considered in the paper: four equal masses connected by six ideal rods. We obtain and discuss the meaning of several important elements, in particular, the constraints and the Hamiltonian vector fields that define the dynamics of the system, the constraint manifold, gauge symmetries, gauge orbits, gauge fixing, and the reduced phase space. |
Title: Uncovering the effective spacetime: Lessons from the effective field theory rationale. Authors: Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay. Journal-ref: Int. J. Mod. Phys. D 24, 1544019 (2015) . Abstract: The cosmological constant problem can be understood as the failure of the decoupling principle behind effective field theory, so that some quantities in the low-energy theory are extremely sensitive to the high-energy properties. While this reflects the genuine character of the cosmological constant, finding an adequate effective field theory framework which avoids this naturalness problem may represent a step forward to understand nature. Following this intuition, we consider a minimal modification of the structure of general relativity which as an effective theory permits to work consistently at low energies, i.e., below the quantum gravity scale. This effective description preserves the classical phenomenology of general relativity and the particle spectrum of the standard model, at the price of changing our conceptual and mathematical picture of spacetime. |
Title: Quantum frictionless trajectories versus geodesics. Authors: Luis C. Barbado, Carlos Barceló, Luis J. Garay. Journal-ref: Phys. Rev. D 92, 084031 (2015) . Abstract: Moving particles outside a star will generally experience quantum friction caused by the Unruh radiation reaction. There exist however radial trajectories that lack this effect (in the outgoing radiation sector, and ignoring backscattering). Along these trajectories, observers perceive just stellar emission, without further contribution from the Unruh effect. They turn out to have the property that the variations of the Doppler and the gravitational shifts compensate each other. They are not geodesics, and their proper acceleration obeys an inverse square law, which means that it could in principle be generated by outgoing stellar radiation. In the case of a black hole emitting Hawking radiation, this may lead to a buoyancy scenario. The ingoing radiation sector has little effect and seems to slow down the fall even further. |
Title: Cosmological Signatures of Anisotropic Spatial Curvature. Authors: Thiago S. Pereira, Guillermo A. Mena Marugán, Saulo Carneiro. Journal-ref: JCAP 1507 (2015) 029 . Abstract: If one is willing to give up the cherished hypothesis of spatial isotropy, many interesting cosmological models can be developed beyond the simple anisotropically expanding scenarios. One interesting possibility is presented by shear-free models in which the anisotropy emerges at the level of the curvature of the homogeneous spatial sections, whereas the expansion is dictated by a single scale factor. We show that such models represent viable alternatives to describe the large-scale structure of the inflationary universe, leading to a kinematically equivalent Sachs-Wolfe effect. Through the definition of a complete set of spatial eigenfunctions we compute the two-point correlation function of scalar perturbations in these models. In addition, we show how such scenarios would modify the spectrum of the CMB assuming that the observations take place in a small patch of a universe with anisotropic curvature. |
Title: Modified FRW cosmologies arising from states of the hybrid quantum Gowdy model. Authors: Beatriz Elizaga Navascués, Mercedes Martín-Benito, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 92 (2015) 024007 . Abstract: We construct approximate solutions of the hybrid quantum Gowdy cosmology with three-torus topology, linear polarization, and local rotational symmetry, in the presence of a massless scalar field. More specifically, we determine some families of states for which the complicated inhomogeneous and anisotropic Hamiltonian constraint operator of the Gowdy model is approximated by a much simpler one. Our quantum states follow the dynamics governed by this simpler constraint, while being at the same time also approximate solutions of the full Gowdy model. This is so thanks to the quantum correlations that the considered states present between the isotropic and anisotropic sectors of the model. Remarkably, this simpler constraint can be regarded as that of a flat Friedmann-Robertson-Walker universe filled with different kinds of perfect fluids and geometrically corrected by homogeneous and isotropic curvature-like terms. Therefore, our quantum states, which are intrinsically inhomogeneous, admit approximate homogeneous and isotropic effective descriptions similar to those considered in modified theories of gravity. |
Title: What can quantum cosmology say about the inflationary universe? Authors: Gianluca Calcagni, Claus Kiefer, Christian F. Steinwachs. Journal-ref: Journal of Physics: Conference Series 626, 012003 (2015) . Abstract: We propose a method to extract predictions from quantum cosmology for inflation that can be confronted with observations. Employing the tunneling boundary condition in quantum geometrodynamics, we derive a probability distribution for the inflaton field. A sharp peak in this distribution can be interpreted as setting the initial conditions for the subsequent phase of inflation. In this way, the peak sets the energy scale at which the inflationary phase has started. This energy scale must be consistent with the energy scale found from the inflationary potential and with the scale found from a potential observation of primordial gravitational waves. Demanding a consistent history of the universe from its quantum origin to its present state, which includes decoherence, we derive a condition that allows one to constrain the parameter space of the underlying model of inflation. We demonstrate our method by applying it to two models: Higgs inflation and natural inflation. |
arXives:1503.03907
Date: 12 Mar 2015
Subject: Cosmological perturbations in LQC
Comments: Reg. article
Title: Gauge-Invariant Perturbations in Hybrid Quantum Cosmology. Authors: Laura Castelló Gomar, Mercedes Martín-Benito, Guillermo A. Mena Marugán. Journal-ref: JCAP 1506 (2015) 06, 045 . Abstract: We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schr\"odinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations. |
Title: Some not-so-common ideas about gravity. Authors: Raúl Carballo-Rubio, Carlos Barceló, Luis J. Garay. Journal-ref: Journal of Physics: Conference Series 626, 012010 (2015). Abstract: Most of the approaches to the construction of a theory of quantum gravity share some principles which do not have specific experimental support up to date. Two of these principles are relevant for our discussion: (i) the gravitational field should have a quantum description in certain regime, and (ii) any theory of gravity containing general relativity should be relational. We study in general terms the possible implications of assuming deviations from these principles, their compatibility with current experimental knowledge, and how can they affect future experiments. |
Title: Quantization of scalar fields coupled to point-masses. Authors: J. Fernando Barbero G., Benito A. Juárez-Aubry, Juan Margalef-Bentabol, Eduardo J. S. Villaseñor. Journal-ref: Class. Quantum Grav. 32, 245009 (2015). Abstract: We study the Fock quantization of a compound classical system consisting of point masses and a scalar field. We consider the Hamiltonian formulation of the model by using the geometric constraint algorithm of Gotay, Nester and Hinds. By relying on this Hamiltonian description, we characterize in a precise way the real Hilbert space of classical solutions to the equations of motion and use it to rigorously construct the Fock space of the system. We finally discuss the structure of this space, in particular the impossibility of writing it in a natural way as a tensor product of Hilbert spaces associated with the point masses and the field, respectively. |
Title: Violation of the strong Huygen's principle and timelike signals from the early Universe. Authors: Ana Blasco, Luis J. Garay, Mercedes Martín-Benito, Eduardo Martín-Martínez. Journal-ref: Phys. Rev. Lett. 114, 141103 (2015). Abstract: We analyze the implications of the violations of the strong Huygens principle in the transmission of information from the early universe to the current era via massless fields. We show that much more information reaches us through timelike channels (not mediated by real photons) than it is carried by rays of light, which are usually regarded as the only carriers of information. |
Title: Dimensional flow in discrete quantum geometries. Authors: Gianluca Calcagni, Daniele Oriti, Johannes Thürigen. Journal-ref: Phys. Rev. D 91, 084047 (2015) . Abstract: In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension d at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is well understood in continuum approaches, in theories built on discrete structures a firm control of the underlying mechanism is still missing. We shed some light on the issue by presenting a particular class of quantum geometries with a flow in the spectral dimension, given by superpositions of states defined on regular complexes. For particular superposition coefficients parametrized by a real number 0<α<d, we find that the spatial spectral dimension reduces to ds≃α at small scales. The spatial Hausdorff dimension of such class of states varies between 1 and d, while the walk dimension takes the usual value dw=2. Therefore, these quantum geometries may be considered as fractal only when α=1, where the "magic number" dsspacetime≃2 for the spectral dimension of space\emph{time}, appearing so often in quantum gravity, is reproduced as well. These results apply, in particular, to special superpositions of spin-network states in loop quantum gravity, and they provide more solid indications of dimensional flow in this approach. |
Title: The Quantum Echo of the Early Universe. Authors: Ana Blasco, Luis J. Garay, Mercedes Martin-Benito, Eduardo Martin-Martinez. Journal-ref: Canadian Journal of Physics, 10.1139 (2014). Abstract: We show that the fluctuations of quantum fields as seen by late comoving observers are significantly influenced by the history of the early Universe, and therefore they transmit information about the nature of spacetime in timescales when quantum gravitational effects were non-negligible. We discuss how this may be observable even nowadays, and thus used to build falsifiability tests of quantum gravity theories. |
Title: Correlations across horizons in quantum cosmology. Authors: Ana Alonso-Serrano, Luis J. Garay, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 90, 124074 (2014). Abstract: Different spacetime regions separated by horizons are not related to each other. We know that this statement holds for classical spacetimes. In this paper we carry out a canonical quantization of a Kantowski-Sachs minisuperspace model whose classical solutions exhibit both an event horizon and a cosmological horizon in order to check whether the above statement also holds from the quantum gravitational point of view. Our analysis shows that in fact this is not the case: Quantum gravitational states with support in spacetime configurations that exclusively describe either the region between horizons or outside them are not consistent in the sense that there exist unitary operators describing a natural notion of evolution that connect them. In other words, unitarity is only preserved in this quantization when dealing with the whole spacetime and not in each region separately. |
Title: Modeling effective FRW cosmologies with perfect fluids from states of the hybrid quantum Gowdy model. Authors: Beatriz Elizaga Navascués, Mercedes Martín-Benito, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 91, 024028 (2015). Abstract: We employ recently developed approximation methods in the hybrid quantization of the Gowdy T^{3} model with linear polarization and a massless scalar field to obtain physically interesting solutions of this inhomogeneous cosmology. More specifically, we propose approximate solutions of the quantum Gowdy model constructed in such a way that, for the Hamiltonian constraint, they effectively behave as those corresponding to a flat homogeneous and isotropic universe filled with a perfect fluid, even though these quantum states are far from being homogeneous and isotropic. We analyze how one can get different perfect fluid effective behaviors, including the cases of dust, radiation, and cosmological constant. |
Title: The lifetime problem of evaporating black holes: mutiny or resignation. Authors: Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay, Gil Jannes. Journal-ref: Class. Quantum Grav. 32 035012 (2015). Abstract: It is logically possible that regularly evaporating black holes exist in nature. In fact, the prevalent theoretical view is that these are indeed the real objects behind the curtain in astrophysical scenarios. There are several proposals for regularizing the classical singularity of black holes so that their formation and evaporation do not lead to information-loss problems. One characteristic is shared by most of these proposals: these regularly evaporating black holes present long-lived trapping horizons, with absolutely enormous evaporation lifetimes in whatever measure. Guided by the discomfort with these enormous and thus inaccessible lifetimes, we elaborate here on an alternative regularization of the classical singularity, previously proposed by the authors in an emergent gravity framework, which leads to a completely different scenario. In our scheme the collapse of a stellar object would result in a genuine time-symmetric bounce, which in geometrical terms amounts to the connection of a black-hole geometry with a white-hole geometry in a regular manner. The two most differential characteristics of this proposal are: i) the complete bouncing geometry is a solution of standard classical general relativity everywhere except in a transient region that necessarily extends beyond the gravitational radius associated with the total mass of the collapsing object; and ii) the duration of the bounce as seen by external observers is very brief (fractions of milliseconds for neutron-star-like collapses). This scenario motivates the search for new forms of stellar equilibrium different from black holes. In a brief epilogue we compare our proposal with a similar geometrical setting recently proposed by Haggard and Rovelli. |
Title: Loop quantum cosmology from group field theory. Authors: Gianluca Calcagni. Journal-ref: Phys. Rev. D 90, 064047 (2014). Abstract: We show that the effective dynamics of the recently proposed isotropic condensate state of group field theory with Laplacian kinetic operator can be equivalent to that of homogeneous and isotropic loop quantum cosmology in the improved dynamics quantization scheme, where the area of elementary holonomy plaquettes is constant. This constitutes a somewhat surprising example of a cosmological model of quantum gravity where the operations of minisuperspace symmetry reduction and quantization can actually commute. |
Title: Electromagnetism as an emergent phenomenon: a step-by-step guide. Authors: Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay, Gil Jannes. Journal-ref: New J. Phys. 16, 123028 (2014). Abstract: We give a detailed description of electrodynamics as an emergent theory from condensed-matter-like structures, not only per se but also as a warm-up for the study of the much more complex case of gravity. We will concentrate on two scenarios that, although qualitatively different, share some important features, with the idea of extracting the basic generic ingredients that give rise to emergent electrodynamics and, more generally, to gauge theories. We start with Maxwell's mechanical model for electrodynamics, where Maxwell's equations appear as dynamical consistency conditions. We next take a superfluid ^{3}He-like system as representative of a broad class of fermionic quantum systems whose low-energy physics reproduces classical electrodynamics (Dirac and Maxwell equations as dynamical low-energy laws). An important lesson that can be derived from both analyses is that the vector potential has a microscopic physical reality and that it is only in the low-energy regime that this physical reality is blurred in favour of gauge invariance, which in addition turns out to be secondary to effective Lorentz invariance. |
arXives:1407.1391
Date: 5 Jul 2014
Subject: White holes
Comments: Honorable mention in the 2014 Gravity Research Foundation essay competition.
Title: Mutiny at the White-Hole District. Authors: Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay. Journal-ref: Int. J. Mod. Phys. 23, 1442022 (2014).. Abstract: The white-hole sector of Kruskal's solution is almost never used in physical applications. However, it might contain the solution to many of the problems associated with gravitational collapse and evaporation. This essay tries to draw attention to some bouncing geometries that make a democratic use of the black- and white-hole sectors. We will argue that these types of behaviour could be perfectly natural in some approaches to the next physical level beyond classical general relativity. |
arXives:1407.0998
Date: 3 Jul 2014
Subject: Cosmological perturbations in LQG
Comments: Reg. article
Title: Cosmological perturbations in hybrid loop quantum cosmology: Mukhanov-Sasaki variables. Authors: Laura Castelló Gomar, Mikel Fernández-Méndez, Guillermo A. Mena Marugán, Javier Olmedo. Journal-ref: Phys. Rev. D 90, 064015 (2014). Abstract: We study cosmological perturbations in the framework of Loop Quantum Cosmology, using a hybrid quantization approach and Mukhanov-Sasaki variables. The formulation in terms of these gauge invariants allows one to clarify the independence of the results on choices of gauge and facilitates the comparison with other approaches proposed to deal with cosmological perturbations in the context of Loop Quantum Theory. A kind of Born-Oppenheimer ansatz is employed to extract the dynamics of the inhomogeneous perturbations, separating them from the degrees of freedom of the Friedmann-Robertson-Walker geometry. With this ansatz, we derive an approximate Schrödinger equation for the cosmological perturbations and study its range of validity. We also prove that, with an alternate factor ordering, the dynamics deduced for the perturbations is similar to the one found in the so-called "dressed metric approach", apart from a possible scaling of the matter field in order to preserve its unitary evolution in the regime of Quantum Field Theory in a curved background and some quantization prescription issues. Finally, we obtain the effective equations that are naturally associated with the Mukhanov-Sasaki variables, both with and without introducing the Born-Oppenheimer ansatz, and with the different factor orderings that we have studied. |
Title: Topology of the Misner Space and its g-boundary. Authors: Juan Margalef-Bentabol, Eduardo J.S. Villaseñor. Journal-ref: General Relativity and Gravitation, 46:1755 (2014). Abstract: The Misner space is a simplified 2-dimensional model of the 4-dimensional Taub-NUT space that reproduces some of its pathological behaviours. In this paper we provide an explicit base of the topology of the complete Misner space R^{1,1}/boost. Besides we prove that some parts of this space, that behave like topological boundaries, are equivalent to the g-boundaries of the Misner space. |
Title: Quantum cosmological consistency condition for inflation. Authors: Gianluca Calcagni, Claus Kiefer, Christian F. Steinwachs. Journal-ref: JCAP 10 (2014) 026. Abstract: We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consistency condition for inflationary models that guarantees compatibility with a tunneling origin and can lead to a testable quantum cosmological prediction. The general method is demonstrated explicitly for the model of natural inflation. |
Title: Nonlocal quantum gravity and M-theory. Authors: Gianluca Calcagni, Leonardo Modesto. Journal-ref: Phys. Rev. D 91, 124059 (2015). Abstract: We construct a ultraviolet completion of the bosonic sector of 11-dimensional supergravity motivated by string field theory. We start from a general class of theories characterized by an entire nonpolynomial form factor which allows one to avoid new poles in the propagator and improves the high-energy behavior of the loops amplitudes. Comparing these models with effective string field theory, a unique form factor is selected out. In view of this, we modify 10-dimensional supergravity and finally get a ultraviolet completion of 11-dimensional supergravity by an oxidation process. The result is a candidate for a finite and unitary particle-field limit of M-theory. |
Title: Anomaly-free cosmological perturbations in effective canonical quantum gravity. Authors: Aurelien Barrau, Martin Bojowald, Gianluca Calcagni, Julien Grain, Mikhail Kagan. Journal-ref: JCAP 05, 051 (2015). Abstract: This article lays out a complete framework for an effective theory of cosmological perturbations with corrections from canonical quantum gravity. Since several examples exist for quantum-gravity effects that change the structure of space-time, the classical perturbative treatment must be rethought carefully. The present discussion provides a unified picture of several previous works, together with new treatments of higher-order perturbations and the specification of initial states. |
Title: Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology. Authors: Laura Castelló Gomar, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 89, 084052 (2014). Abstract: We study scalar fields subject to an equation of the Klein-Gordon type in nonstationary spacetimes, such as those found in cosmology, assuming that all the relevant spatial dependence is contained in the Laplacian. We show that the field description—with a specific canonical pair—and the Fock representation for the quantization of the field are fixed indeed in a unique way (except for unitary transformations that do not affect the physical predictions) if we adopt the combined criterion of (a) imposing the invariance of the vacuum under the group of spatial symmetries of the field equations and (b) requiring a unitary implementation of the dynamics in the quantum theory. Besides, we provide a spacetime interpretation of the field equations as those corresponding to a scalar field in a cosmological spacetime that is conformally ultrastatic. In addition, in the privileged Fock quantization, we investigate the generalization of the evolution of physical states from the hyperbolic dynamical regime to an elliptic regime. In order to do this, we contemplate the possibility of processes with signature change in the spacetime where the field propagates and discuss the behavior of the background geometry when the change happens, proving that the spacetime metric degenerates. Finally, we argue that this kind of signature change leads naturally to a phenomenon of particle creation, with exponential production. |
Title: Separable Hilbert space for loop quantization. Authors: J. Fernando Barbero G., Tomasz Pawłowski, Eduardo J. S. Villaseñor. Journal-ref: Phys. Rev. D 90, 067505 (2014). Abstract: We discuss, within the simplified context provided by the polymeric harmonic oscillator, a construction leading to a separable Hilbert space that preserves some of the most important features of the spectrum of the Hamiltonian operator. This construction may be applied to other polymer quantum mechanical systems, including those of loop quantum cosmology, and is likely generalizable to certain formulations of full loop quantum gravity. It is helpful to sidestep some of the physically relevant issues that appear in that context, in particular those related to superselection and the definition of suitable ensembles for the statistical mechanics of these types of systems. |
Date: 11 Mar 2014
Subject: Perturbations in LQC
Comments: Proceedings article
Title: Loop Quantum Cosmological Perturbations. Authors: Mikel Fernández-Méndez, Guillermo A. Mena Marugán, Javier Olmedo. Journal-ref: J. Phys.: Conf. Ser. 490, 012152 (2014). Abstract: In the context of loop quantum cosmology, we provide a complete quantization of an inhomogeneous inflationary model consisting of a perturbed Friedmann-Lemaître-Robertson-Walker universe filled with a minimally coupled massive scalar field. We focus on the case of flat, compact spatial sections. After fixing the local gauge freedom, the kinematical Hilbert space is constructed by combining the representation used in loop quantum cosmology for the homogeneous sector with a preferred Fock quantization of the inhomogeneities. We characterize the physical states annihilated by the quantum Hamiltonian constraint and discuss the evolution of the inhomogeneities in the presence of an emergent relational time. |
Title: Effective dynamics of scalar perturbations in a flat Friedmann-Robertson-Walker spacetime in loop quantum cosmology. Authors: Mikel Fernández-Méndez, Guillermo A. Mena Marugán, Javier Olmedo. Journal-ref: Phys. Rev. D 89, 044041 (2014). Abstract: We study the evolution of a homogeneous and isotropic spacetime for which the spatial sections have three-torus topology, coupled to a massless scalar field with small scalar perturbations within loop quantum cosmology. We consider a proposal for the effective dynamics based on a previous hybrid quantization completed by us. Consequently, we introduce a convenient gauge fixing and adopt reduced canonical variables adapted to that hybrid quantum description. Besides, we keep backreaction contributions on the background coming from terms quadratic in the perturbations in the action of the system. We carry out a numerical analysis assuming that the inhomogeneities were in a massless vacuum state at distant past (where the initial data are set). At distant future, we observe a statistical amplification of the modes amplitude in the infrared region, as well as a phase synchronization arising from quantum gravity phenomena. A description of the perturbations in terms of the Mukhanov–Sasaki gauge invariants provides the same qualitative results. Finally, we analyze some consequences of the backreaction in our effective description. |
Title: Unimodular gravity and general relativity from graviton self-interactions. Authors: Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay. Journal-ref: Phys. Rev. D 89, 124019 (2014). Abstract: It is commonly accepted that general relativity is the only solution to the consistency problem that appears when trying to build a theory of interacting gravitons (massless spin-2 particles). Padmanabhan's 2008 thought-provoking analysis raised some concerns that are having resonance in the community. In this work we present the self-coupling problem in detail and explicitly solve the infinite-iterations scheme associated with it for the simplest theory of a graviton field, which corresponds to an irreducible spin-2 representation of the Poincaré group. We make explicit the non-uniqueness problem by finding an entire family of solutions to the self-coupling problem. Then we show that the only resulting theory which implements a deformation of the original gauge symmetry happens to have essentially the structure of unimodular gravity. This makes plausible the possibility of a natural solution to the first cosmological constant problem in theories of emergent gravity. Later on we change for the sake of completeness the starting free-field theory to Fierz-Pauli theory, an equivalent theory but with a larger gauge symmetry. We indicate how to carry out the infinite summation procedure in a similar way. Overall, we conclude that as long as one requires the (deformed) preservation of internal gauge invariance, one naturally recovers the structure of unimodular gravity or general relativity but in a version that explicitly shows the underlying Minkowski spacetime, in the spirit of Rosen's flat-background bimetric theory. |
Date: 2013
Subject: QG and QC
Comments: Book
Title: Quantum Gravity and Quantum Cosmology. Editors: Gianluca Calcagni, Lefteris Papantonopoulos, George Siopsis, Nikos Tsamis. Journal-ref: Lecture Notes in Physics 863. |
Date: 2013
Subject: Inhomogeneous LQC
Comments: Proceedings article
Title:Inhomogeneous Loop Quantum Cosmology with Matter: Approximate FRW Cosmologies from the Hybrid Gowdy Model with Matter. Authors: Mercedes Martín-Benito, Daniel Martín-de Blas, Guillermo A. Mena Marugán. Journal-ref: Proceedings of the Xth International Conference on Gravitation, Astrophysics and Cosmology (ICGAC10), p. 302-304, eds. R. Triay, J. T. Thanh Vân, and L. M. Celnikier. |
Title: Spectral dimension of quantum geometries. Authors: Gianluca Calcagni, Daniele Oriti, Johannes Thürigen. Journal-ref: Class. Quantum Grav. 31, 135014 (2014). Abstract: The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. |
Title: Strong Planck constraints on braneworld and non-commutative inflation. Authors: Gianluca Calcagni, Sachiko Kuroyanagi, Junko Ohashi, Shinji Tsujikawa. Journal-ref: JCAP 03 (2014) 052. Abstract: We place observational likelihood constraints on braneworld and non-commutative inflation for a number of inflaton potentials, using Planck, WMAP polarization and BAO data. Both braneworld and non-commutative scenarios of the kind considered here are limited by the most recent data even more severely than standard general-relativity models. At more than 95 % confidence level, the monomial potential V(ϕ) ∝ ϕ^{p} is ruled out for p ≥ 2 in the Randall--Sundrum (RS) braneworld cosmology and, for p > 0, also in the high-curvature limit of the Gauss–Bonnet (GB) braneworld and in the infrared limit of non-commutative inflation, due to a large scalar spectral index. Some parameter values for natural inflation, small-varying inflaton models and Starobinsky inflation are allowed in all scenarios, although some tuning is required for natural inflation in a non-commutative spacetime. |
Title: Nonlocality in string theory. Authors: Gianluca Calcagni, Leonardo Modesto. Journal-ref: J. Phys. A: Math. Theor. 47, 355402 (2014). Abstract: We discuss an aspect of string theory which has been tackled from many different perspectives, but incompletely: the role of nonlocality in the theory and its relation to the geometric shape of the string. In particular, we will describe in quantitative terms how one can zoom out from an extended object such as the string in such a way that, at sufficiently large scales, it appears structureless. Since there are no free parameters in free-string theory, the notion of large scales will be unambiguously determined. In other words, we will be able to answer the question: How and at which scale can the string be seen as a particle? In doing so, we will employ the concept of spectral dimension in a new way with respect to its usual applications in quantum gravity. The operational notions of worldsheet and target spacetime dimension in string theory are also clarified and found to be in mutual agreement. |
Title: Singularity avoidance in the hybrid quantization of the Gowdy model. Authors: Paula Tarrío, Mikel Fernández-Méndez, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 88, 084050 (2013). Abstract: One of the most remarkable phenomena in Loop Quantum Cosmology is that, at least for homogeneous cosmological models, the Big Bang is replaced with a Big Bounce that connects our universe with a previous branch without passing through a cosmological singularity. The goal of this work is to study the existence of singularities in Loop Quantum Cosmology including inhomogeneities and check whether the behavior obtained in the purely homogeneous setting continues to be valid. With this aim, we focus our attention on the three-torus Gowdy cosmologies with linearly polarized gravitational waves and use effective dynamics to carry out the analysis. For this model, we prove that all the potential cosmological singularities are avoided, generalizing the results about resolution of singularities to this scenario with inhomogeneities. We also demonstrate that, if a bounce in the (Bianchi background) volume occurs, the inhomogeneities increase the value of this volume at the bounce with respect to its counterpart in the homogeneous case. |
Date: 13 Sep 2013
Subject: BHs
Comments: Proceedings article
Title: Avoiding the Trans-Planckian Problem in Black Hole Physics. Authors: Carlos Barceló, Luis C. Barbado, Luis J. Garay, Gil Jannes. Journal-ref: Springer Proceedings in Mathematics & Statistics. 60, 129 (2014). Abstract: We describe how the avoidance of the trans-Planckian problem of Hawking radiation can be used as a guiding principle in searching for a compelling scenario for the evaporation of black holes or black-hole-like objects. We argue that there exist only three possible scenarios, depending on whether the classical notion of long-lived horizon is preserved by high-energy physics and on whether the dark and compact astrophysical objects that we observe have long-lived horizons in the first place. Some specific findings along the way are (a) that a theory with high-energy superluminal signaling and a long-lived trapping horizon would be extremely unstable in astrophysical terms and (b) that stellar pulsations of objects hovering right outside, but extremely close to their gravitational radius, can result in a mechanism for Hawking emission. |
Date: 13 Sep 2013
Subject: Perturbations in LQC
Comments: Proceedings article
Title: Complete Quantization of Scalar Cosmological Perturbations. Authors: Mikel Fernández-Méndez, Guillermo A. Mena Marugán, Javier Olmedo. Journal-ref: Springer Proceedings in Mathematics & Statistics. 60, 261 (2014). Abstract: We quantize a perturbed Friedmann–Lemaître–Robertson–Walker model coupled to a massive scalar field. We consider only scalar perturbations, in a universe whose spatial sections have the topology of a three-sphere. The local gauge freedom is fixed at the classical level. We choose a preferred parametrization of the system by adapting uniqueness criteria for the quantization of scalar fields with time-dependent mass. The Hilbert space of the theory is constructed combining a polymer representation for the homogeneous background and the preferred Fock quantization for the perturbations. Finally, we propose a prescription to promote the Hamiltonian constraint to a quantum operator, and characterize the states annihilated by it in terms of their initial data at the minimum-volume section. |
Date: 13 Sep 2013
Subject: Inhomogeneous LQC
Comments: Proceedings article
Title: Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization and Approximated Solutions. Authors: Daniel Martín-de Blas, Mercedes Martín-Benito, Guillermo A. Mena Marugán. Journal-ref: Springer Proceedings in Mathematics & Statistics. 60, 327 (2014). Abstract: We study approximation methods to construct physical solutions for the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field. The loop quantization of the Bianchi I background and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical predictions calls for the introduction of well justified approximations. We show that, for specific regimes of physical interest, one can approximate the Hamiltonian constraint by a more simple one and obtain its solutions. |
Title: Echo of the Quantum Bounce. Authors: Luis J. Garay, Mercedes Martín-Benito, Eduardo Martín-Martínez. Journal-ref: Phys. Rev. D 89, 043510 (2014). Abstract: We identify a signature of quantum gravitational effects that survives from the early universe to the current era: Fluctuations of quantum fields as seen by comoving observers are significantly influenced by the history of the early universe. In particular we show how the existence (or not) of a quantum bounce leaves a trace in the background quantum noise that is not damped and would be non-negligible even nowadays. Furthermore, we estimate an upper bound for the typical energy and length scales where quantum effects are relevant. We discuss how this signature might be observed and therefore used to build falsifiability tests of quantum gravity theories. |
Title: Multi-scale gravity and cosmology. Authors: Gianluca Calcagni. Journal-ref: JCAP 12 (2013) 041. Abstract: The gravitational dynamics and cosmological implications of three classes of recently introduced multi-scale spacetimes (with, respectively, ordinary, weighted and q-derivatives) are discussed. These spacetimes are non-Riemannian: the metric structure is accompanied by an independent measure-differential structure with the characteristics of a multi-fractal, namely, different dimensionality at different scales and, at ultra-short distances, a discrete symmetry known as discrete scale invariance. Under this minimal paradigm, five general features arise: (a) the big-bang singularity can be replaced by a finite bounce, (b) the cosmological constant problem is reinterpreted, since accelerating phases can be mimicked by the change of geometry with the time scale, without invoking a slowly rolling scalar field, (c) the discreteness of geometry at Planckian scales can leave an observable imprint of logarithmic oscillations in cosmological spectra and (d) give rise to an alternative mechanism to inflation or (e) to a fully analytic model of cyclic mild inflation, where near scale invariance of the perturbation spectrum can be produced without strong acceleration. Various properties of the models and exact dynamical solutions are discussed. In particular, the multi-scale geometry with weighted derivatives is shown to be a Weyl integrable spacetime. |
Title: Black-hole entropy and minimal diffusion. Authors: Michele Arzano, Gianluca Calcagni. Journal-ref: Phys. Rev. D 88, 084017 (2013). Abstract: The density of states reproducing the Bekenstein-Hawking entropy-area scaling can be modeled via a nonlocal field theory. We define a diffusion process based on the kinematics of this theory and find a spectral dimension whose flow exhibits surprising properties. While it asymptotes four from above in the infrared, in the ultraviolet the spectral dimension diverges at a finite (Planckian) value of the diffusion length, signaling a breakdown of the notion of diffusion on a continuum spacetime below that scale. We comment on the implications of this minimal diffusion scale for the entropy bound in a holographic and field-theoretic context. |
Title: Generalized Stirling permutations and forests: Higher-order Eulerian and Ward numbers. Authors: J. Fernando Barbero G., Jesús Salas, Eduardo J. S. Villaseñor. Journal-ref: Electron. J. Comb. 22 (2015) #P3.37. Abstract: We define a new family of generalized Stirling permutations that can be interpreted in terms of ordered trees and forests. We prove that the number of generalized Stirling permutations with a fixed number of ascents is given by a natural three-parameter generalization of the well-known Eulerian numbers. We give the generating function for this new class of numbers and, in the simplest cases, we find closed formulas for them and the corresponding row polynomials. By using a non-trivial involution our generalized Eulerian numbers can be mapped onto a family of generalized Ward numbers, forming a Riordan inverse pair, for which we also provide a combinatorial interpretation. |
Title: Hybrid quantization of an inflationary model: The flat case. Authors: Mikel Fernández-Méndez, Guillermo A. Mena Marugán, Javier Olmedo. Journal-ref: Phys. Rev. D 88, 044013 (2013). Abstract: We present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are flat and compact, with the topology of a three-torus. The quantization is carried out along the lines that were put forward by the authors in a previous work for spherical topology. The action of the system is truncated at second order in perturbations. The local gauge freedom is fixed at the classical level, although different gauges are discussed and shown to lead to equivalent conclusions. Moreover, descriptions in terms of gauge-invariant quantities are considered. The reduced system is proven to admit a symplectic structure, and its dynamical evolution is dictated by a Hamiltonian constraint. Then, the background geometry is polymerically quantized, while a Fock representation is adopted for the inhomogeneities. The latter is selected by uniqueness criteria adapted from quantum field theory in curved spacetimes, which determine a specific scaling of the perturbations. In our hybrid quantization, we promote the Hamiltonian constraint to an operator on the kinematical Hilbert space. If the zero mode of the scalar field is interpreted as a relational time, a suitable ansatz for the dependence of the physical states on the polymeric degrees of freedom leads to a quantum wave equation for the evolution of the perturbations. Alternatively, the solutions to the quantum constraint can be characterized by their initial data on the minimum-volume section of each superselection sector. The physical implications of this model will be addressed in a future work, in order to check whether they are compatible with observations. |
Title: Bivariate Generating Functions for a Class of Linear Recurrences: General Structure. Authors: J. Fernando Barbero G., Jesús Salas, Eduardo J. S. Villaseñor. Journal-ref: J. Combin. Theory A 125, 146 (2014). Abstract: We consider Problem 6.94 posed in the book Concrete Mathematics by Graham, Knuth, and Patashnik, and solve it by using bivariate exponential generating functions. The family of recurrence relations considered in the problem contains many cases of combinatorial interest for particular choices of the six parameters that define it. We give a complete classification of the partial differential equations satisfied by the exponential generating functions, and solve them in all cases. We also show that the recurrence relations defining the combinatorial numbers appearing in this problem display an interesting degeneracy that we study in detail. Finally, we obtain for all cases the corresponding univariate row generating polynomials. |
Title: Approximation methods in loop quantum cosmology: from Gowdy cosmologies to inhomogeneous models in Friedmann–Robertson–Walker geometries. Authors: Mercedes Martín-Benito, Daniel Martín-de Blas, Guillermo A. Mena Marugán. Journal-ref: Class. Quantum Grav. 31, 075022 (2014). Abstract: We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of three-torus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, corresponding to Bianchi I geometries, as if it described a Friedmann–Robertson–Walker (FRW) model corrected with anisotropies. This approximation is valid in the sector of high energies of the FRW geometry (concerning its contribution to the constraint) and for anisotropy profiles that are sufficiently smooth. In addition, for certain families of states related to regimes of physical interest, with negligible quantum effects of the anisotropies and small inhomogeneities, one can approximate the Hamiltonian constraint of the inhomogeneous system by that of an FRW geometry with a relatively simple matter content, and then obtain its solutions. |
arXives:1306.5854
Date: 25 Jun 2013
Subject: Hamiltonian mechanics
Comments: Reg. article. Highlights of 2013-2014 in quantum gravity.
Title: Hamiltonian treatment of linear field theories in the presence of boundaries: a geometric approach. Authors: J. Fernando Barbero G., Jorge Prieto, Eduardo J. S. Villaseñor. Journal-ref: Class. Quantum Grav. 31, 045021 (2014). Abstract: The purpose of this paper is to study in detail the constraint structure of the Hamiltonian and symplectic-Lagrangian descriptions for the scalar and electromagnetic fields in the presence of spatial boundaries. We carefully discuss the implementation of the geometric constraint algorithm of Gotay, Nester and Hinds with special emphasis on the relevant functional analytic aspects of the problem. This is an important step towards the rigorous understanding of general field theories in the presence of boundaries, very especially when these fail to be regular. The geometric approach developed in the paper is also useful with regard to the interpretation of the physical degrees of freedom and the nature of the constraints when both gauge symmetries and boundaries are present. |
Title: Relativistic particle in multiscale spacetimes. Authors: Gianluca Calcagni. Journal-ref: Phys. Rev. D 88, 065005 (2013). Abstract: We study the action and the dynamics of a relativistic particle, uncharged or charged, in multiscale spacetimes. Invariance under reparametrizations and Poincar\'e symmetries uniquely determine the action and the line element to be the usual ones, without the weight factors typical of particle mechanics in these geometries. The resulting spacetime is multiscale only along spatial directions. This version of the system is also dictated by recovery of the nonrelativistic limit together with compatibility with Maxwell and electrodynamics field theory. Giving up all these requirements and allowing for a nontrivial weight factor in the time direction produces a modified line element and considerably complicates the dynamics in the case of a charged particle. |
Title: Super-accelerating bouncing cosmology in asymptotically-free non-local gravity. Authors: Gianluca Calcagni, Leonardo Modesto, Piero Nicolini. Journal-ref: Eur. Phys. J. C 74, 2999 (2014). Abstract: Recently, evidence has been collected that a class of gravitational theories with certain non-local operators is renormalizable. We consider one such model which, at the linear perturbative level, reproduces the effective non-local action for the light modes of bosonic closed string-field theory. Using the property of asymptotic freedom in the ultraviolet and fixing the classical behavior of the scale factor at late times, an algorithm is proposed to find general homogeneous cosmological solutions valid both at early and late times. Imposing a power-law classical limit, these solutions (including anisotropic ones) display a bounce, instead of a big-bang singularity, and super-accelerate near the bounce even in the absence of an inflaton or phantom field. |
Title: Quantum field theory with varying couplings. Authors: Gianluca Calcagni, Giuseppe Nardelli. Journal-ref: Int. J. Mod. Phys. A 29, 1450012 (2014). Abstract: A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific choice of the coupling's profile for any finite-order perturbative expansion. For one of these cases, some tree and one-loop diagrams are calculated. This is an example of a theory where violation of Lorentz symmetry is not enhanced at the quantum level. We draw some consequences for the renormalization properties of certain classes of fractional field theories. |
Title: Band structure in the polymer quantization of the harmonic oscillator Authors: J. Fernando Barbero G., Jorge Prieto, Eduardo J. S. Villaseñor. Journal-ref: Class. Quantum Grav. 30, 165011 (2013). Abstract: We discuss the detailed structure of the spectrum of the Hamiltonian for the polymerized harmonic oscillator and compare it with the spectrum in the standard quantization. As we will see the non-separability of the Hilbert space implies that the point spectrum consists of bands similar to the ones appearing in the treatment of periodic potentials. This feature of the spectrum of the polymeric harmonic oscillator may be relevant for the discussion of the polymer quantization of the scalar field and may have interesting consequences for the statistical mechanics of these models. |
Title: Varying electric charge in multiscale spacetimes. Authors: Gianluca Calcagni, Joao Magueijo, David Rodríguez Fernández. Journal-ref: Phys. Rev. D 89, 024021 (2014). Abstract: We derive the covariant equations of motion for Maxwell field theory and electrodynamics in multiscale spacetimes with weighted Laplacian. An effective spacetime-dependent electric charge of geometric origin naturally emerges from the theory, thus giving rise to a varying fine-structure constant. The theory is compared with other varying-coupling models, such as those with a varying electric charge or varying speed of light. The theory is also confronted with cosmological observations, which can place constraints on the characteristic scales in the multifractional measure. We note that the model considered here is fundamentally different from those previously proposed in the literature, either of the varying-e or varying-c persuasion. |
Title: Probing the quantum nature of spacetime by diffusion. Authors: Gianluca Calcagni, Astrid Eichhorn, Frank Saueressig. Journal-ref: Phys. Rev. D 87, 124028 (2013). Abstract: Many approaches to quantum gravity have resorted to diffusion processes to characterize the spectral properties of the resulting quantum spacetimes. We critically discuss these quantum-improved diffusion equations and point out that a crucial property, namely positivity of their solutions, is not preserved automatically. We then construct a novel set of diffusion equations with positive semi-definite probability densities, applicable to Asymptotically Safe gravity, Horava-Lifshitz gravity and Loop Quantum Gravity. These recover all previous results on the spectral dimension and shed further light on the structure of the quantum spacetimes by assessing the underlying stochastic processes. Pointing out that manifestly different diffusion processes lead to the same spectral dimension, we propose the probability distribution of the diffusion process as a refined probe of quantum spacetime. |
Title: Spectral dimension and diffusion in multi-scale spacetimes. Authors: Gianluca Calcagni, Giuseppe Nardelli. Journal-ref: Phys. Rev. D 88, 124025 (2013). Abstract: Starting from a classical-mechanics stochastic model encoded in a Langevin equation, we derive the natural diffusion equation associated with three classes of multiscale spacetimes (with weighted, ordinary, and "q-Poincaré" symmetries). As a consistency check, the same result is obtained by inspecting the propagation of a quantum-mechanical particle in a disordered environment. The solution of the diffusion equation displays a time-dependent diffusion coefficient and represents a probabilistic process, classified according to the statistics of the noise in the Langevin equation. We thus illustrate, also with pictorial aids, how spacetime geometries can be more completely catalogued not only through their Hausdorff and spectral dimension, but also by a stochastic process. The spectral dimension of multifractional spacetimes is then computed and compared with what was found in previous studies, where a diffusion equation with some open issues was assumed rather than derived. These issues are here discussed and solved, and they point towards the model with q-Poincaré symmetries. |
Date: 8 Feb 2013
Subject: Cosmological perturbations
Comments: Proceedings article
Title: Unitary evolution and uniqueness of the Fock quantization in flat cosmologies. Authors: Guillermo A. Mena Marugán, Daniel Martín-de Blas, Laura Castelló Gomar. Journal-ref: J. Phys.: Conf. Ser. 410, 012151 (2013). Abstract: We study the Fock quantization of scalar fields with a time dependent mass in cosmological scenarios with flat compact spatial sections. This framework describes physically interesting situations like, e.g., cosmological perturbations in flat Friedmann-Robertson-Walker spacetimes, generally including a suitable scaling of them by a background function. We prove that the requirements of vacuum invariance under the spatial isometries and of a unitary quantum dynamics select (a) a unique canonical pair of field variables among all those related by time dependent canonical transformations which scale the field configurations, and (b) a unique Fock representation for the canonical commutation relations of this pair of variables. The proof is generalizable to any compact spatial topology in three or less dimensions, though we focus on the case of the three-torus owing to the especially relevant implications. |
Date: 22 Jan 2013
Subject: Dark energy
Comments: Reg. article
Title: Why is the running vacuum energy more benign than the holographic Ricci dark energy? Authors: Mariam Bouhmadi-López, Yaser Tavakoli. Journal-ref: Phys. Rev. D 87, 023515 (2013). Abstract: A very interesting generalization of the running vacuum energy density has been recently advanced [S. Basilakos, D. Polarski, and J. Sola, Phys. Rev. D 86, 043010 (2012)]. The Friedmann equation of this model looks pretty much similar to that of a homogeneous and isotropic universe filled with an holographic Ricci dark energy (HRDE) component. Despite the analogy between these two models, it turns out that one of them, generalization of the running vacuum energy, is singularity-free in the future while the other, HRDE, is not. Indeed, a universe filled with an HRDE component can hit, for example, a big rip singularity. We clarify this issue by solving analytically the Friedmann equation for both models and analyzing the role played by the local conservation of the energy density of the different components when filling the universe. In addition, not everything is bad news about the HRDE. In fact, we point out that in some particular cases the HRDE, when endowed with a negative cosmological constant and in the absence of an explicit dark matter component, can mimic dark matter and explain the late-time cosmic acceleration of the universe through an asymptotically de Sitter universe. |
Title: Massless scalar field in de Sitter spacetime: unitary quantum time evolution. Authors: Jerónimo Cortez, Daniel Martín-de Blas, Guillermo A. Mena Marugán, Jose M. Velhinho. Journal-ref: Class. Quantum Grav. 30, 075015 (2013). Abstract: We prove that, under the standard conformal scaling, a massless field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. This result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch-Davies vacuum. |
Title: Unitary evolution and uniqueness of the Fock quantization in flat cosmologies with compact spatial sections. Authors: Laura Castelló Gomar, Jerónimo Cortez, Daniel Martín-de Blas, Guillermo A. Mena Marugán, José. M. Velhinho. Journal-ref: EJTP 11, 43 (2014). Abstract: We study the Fock quantization of scalar fields with a time dependent mass in cosmological scenarios with flat compact spatial sections. This framework describes physically interesting situations like, e.g., cosmological perturbations in flat Friedmann-Robertson-Walker spacetimes, generally including a suitable scaling of them by a background function. We prove that the requirements of vacuum invariance under the spatial isometries and of a unitary quantum dynamics select (a) a unique canonical pair of field variables among all those related by time dependent canonical transformations which scale the field configurations, and (b) a unique Fock representation for the canonical commutation relations of this pair of variables. Though the proof is generalizable to other compact spatial topologies in three or less dimensions, we focus on the case of the three-torus owing to its relevance in cosmology, paying a especial attention to the role played by the spatial isometries in the determination of the representation. |
Title: Uniqueness of the Fock quantization of scalar fields under mode preserving canonical transformations varying in time. Authors: Jerónimo Cortez, Lucía Fonseca, Daniel Martín-de Blas, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 87, 044013 (2013). Abstract: We study the Fock quantization of scalar fields of Klein-Gordon type in nonstationary scenarios propagating in spacetimes with compact spatial sections, allowing for different field descriptions that are related by means of certain nonlocal linear canonical transformations that depend on time. More specifically, we consider transformations that do not mix eigenmodes of the Laplace-Beltrami operator, which are supposed to be dynamically decoupled. In addition, we assume that the canonical transformations admit an asymptotic expansion for large eigenvalues (in norm) of the Laplace-Beltrami operator in the form of a series of half integer powers. Canonical transformations of this kind are found in the study of scalar perturbations in inflationary cosmologies, relating for instance the physical degrees of freedom of these perturbations after gauge fixing with gauge invariant canonical pairs of Bardeen quantities. We characterize all possible transformations of this type and show that, independently of the initial field description, the combined criterion of requiring (i) invariance of the vacuum under the spatial symmetries and (ii) a unitary implementation of the dynamics, leads to a unique equivalence class of Fock quantizations, all of them related by unitary transformations. This conclusion provides even further robustness to the validity of the proposed criterion, completing the results that have already appeared in the literature about the uniqueness of the Fock quantization under changes of field description when one permits exclusively local time dependent canonical transformations that scale the field configuration. |
Title: Slow-Roll Inflation Preceded by a Topological Defect Phase à la Chaplygin Gas. Authors: Mariam Bouhmadi-Lopez, Pisin Chen, Yu-Chien Huang, Yu-Hsiang Lin. Journal-ref: Phys. Rev. D 87, 103513 (2013). Abstract: We present a simple toy model corresponding to a network of frustrated topological defects of domain walls or cosmic strings that exist previous to the standard slow-roll inflationary era of the universe. Such a network (i) can produce a slower inflationary era than that of the standard scenario if it corresponds to a network of frustrated domain walls or (ii) can induce a vanishing universal acceleration; i. e., the universe would expand at a constant speed, if it corresponds to a network of frustrated cosmic strings red. Those features are phenomenologically modeled by a Chaplygin gas that can interpolate between a network of frustrated topological defects and a de Sitter-like or a power-law inflationary era. We show that this scenario can alleviate the quadruple anomaly of the cosmic microwave background spectrum. Using the method of the Bogoliubov coefficients, we obtain the spectrum of the gravitational waves as would be measured today for the whole range of frequencies. We comment on the possible detection of this spectrum by the planned detectors like BBO and DECIGO. |
Title: Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes. Authors: Laura Castelló Gomar, Jerónimo Cortez, Daniel Martín-de Blas, Guillermo A. Mena Marugán, José M. Velhinho. Journal-ref: JCAP 11(2012) 001. Abstract: We study the Fock quantization of scalar fields in (generically) time dependent scenarios, focusing on the case in which the field propagation occurs in –either a background or effective– spacetime with spatial sections of flat compact topology. The discussion finds important applications in cosmology, like e.g. in the description of test Klein-Gordon fields and scalar perturbations in Friedmann-Robertson-Walker spacetime in the observationally favored flat case. Two types of ambiguities in the quantization are analyzed. First, the infinite ambiguity existing in the choice of a Fock representation for the canonical commutation relations, understandable as the freedom in the choice of inequivalent vacua for a given field. Besides, in cosmological situations, it is customary to scale the fields by time dependent functions, which absorb part of the evolution arising from the spacetime, which is treated classically. This leads to an additional ambiguity, this time in the choice of a canonical pair of field variables. We show that both types of ambiguities are removed by the requirements of (a) invariance of the vacuum under the symmetries of the three-torus, and (b) unitary implementation of the dynamics in the quantum theory. In this way, one arrives at a unique class of unitarily equivalent Fock quantizations for the system. This result provides considerable robustness to the quantum predictions and renders meaningful the confrontation with observation. |
Title: Symmetries and propagator in multifractional scalar field theory. Authors: Gianluca Calcagni, Giuseppe Nardelli. Journal-ref: Phys. Rev. D 87, 085008 (2013). Abstract: The symmetries of a scalar field theory in multifractional spacetimes are analyzed. The free theory realizes the Poincaré algebra, and the associated symmetries are modifications of ordinary translations and Lorentz transformations. In the interacting case, the Poincaré algebra is broken by interaction terms. The Feynman propagator of the scalar field is computed and found to possess the usual mass poles. As a consequence of these findings, the mass of a particle is a well-defined concept at all scales, and a perturbative quantum theory can be constructed. |
Title: Smoking guns of a bounce in modified theories of gravity through the spectrum of the gravitational waves. Authors: Mariam Bouhmadi-Lopez, Joao Morais, Alfredo B. Henriques. Journal-ref: Phys. Rev. D 87, 103528 (2013). Abstract: We present an inflationary model preceded by a bounce in a metric theory à la f(R) where R is the scalar curvature of the space-time. The model is asymptotically de Sitter such that the gravitational action tends asymptotically to a Hilbert-Einstein action, therefore modified gravity affects only the early stages of the universe. We then analyse the spectrum of the gravitational waves through the method of the Bogoliubov coefficients by two means: taking into account the gravitational perturbations due to the modified gravitational action in the f(R) setup and by simply considering those perturbations inherent to the standard Hilbert-Einstein action. We show that there are distinctive (oscillatory) signals on the spectrum for very low frequencies; i.e. corresponding to modes that are currently entering the horizon. |
Title: Multifractional spacetimes, asymptotic safety and Hořava-Lifshitz gravity. Authors: Gianluca Calcagni. Journal-ref: Int. J. Mod. Phys. A 28, 1350092 (2013). Abstract: We compare the recently formulated multifractional spacetimes with field theories of quantum gravity based on the renormalization group (RG), such as asymptotic safety and Hořava–Lifshitz gravity. The change of spacetime dimensionality with the probed scale is realized in both cases by an adaptation of the measurement tools ("rods") to the scale, but in different ways. In the multifractional case, by an adaptation of the position-space measure, which can be encoded into an explicit scale dependence of effective coordinates. In the case of RG-based theories, by an adaptation of the momenta. The two pictures are mapped into each other, thus presenting the fractal structure of spacetime in RG-based theories under an alternative perspective. |
arXives: 1209.1110
Date: 5 Sep 2012
Subject: Multifracional spacetimes
Comments: Proceedings article
Title: Introduction to multifractional spacetimes. Authors: Gianluca Calcagni. Journal-ref: AIP Conf. Proc. 1483, 314 (2012). Abstract: We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display discrete symmetries in the ultraviolet and ordinary Poincaré symmetries in the infrared. Under certain reasonable assumptions, field theories (including gravity) on multifractional geometries are generally argued to be perturbatively renormalizable. We also sketch the relation with other field theories of quantum gravity based on the renormalization group. |
Title: Observational effects from quantum cosmology. Authors: Gianluca Calcagni. Journal-ref: Ann. Phys. (Berlin) 525, 323 (2013). Abstract: The status of quantum cosmologies as testable models of the early universe is assessed in the context of inflation. While traditional Wheeler-DeWitt quantization is unable to produce sizable effects in the cosmic microwave background, the more recent loop quantum cosmology can generate potentially detectable departures from the standard cosmic spectrum. Thus, present observations constrain the parameter space of the model, which could be made falsifiable by near-future experiments. |
Title: Laplacians on discrete and quantum geometries. Authors: Gianluca Calcagni, Daniele Oriti, Johannes Thürigen. Journal-ref: Class. Quantum Grav. 30, 125006 (2013). Abstract: We extend discrete calculus for arbitrary (p-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries. |
Title: Quantum mechanics in fractional and other anomalous spacetimes. Authors: Gianluca Calcagni, Giuseppe Nardelli, Marco Scalisi. Journal-ref: J. Math. Phys. 53, 102110 (2012). Abstract: We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the wave-functions minimizing the uncertainty are found. In spite of the fact that ordinary time and spatial translations are broken and the dynamics is not unitary, the theory is in one-to-one correspondence with a unitary one, thus allowing us to employ standard tools of analysis. These features are illustrated in the examples of the free particle and the harmonic oscillator. While fractional (and the more general anomalous-spacetime) free models are formally indistinguishable from ordinary ones at the classical level, at the quantum level they differ both in the Hilbert space and for a topological term fixing the classical action in the path integral formulation. Thus, all non-unitarity in fractional quantum dynamics is encoded in a contribution depending only on the initial and final state. |
Date: 7 Jul 2012
Subject: BH in LQG
Comments: Proceedings article
Title: Black holes: combinatorics and the thermodynamic limit. Authors: J. Fernando Barbero G. Journal-ref: AIP Conf. Proc. 1458, 23 (2012). Abstract: The purpose of this contribution is to review the combinatorial methods used in loop quantum gravity to compute the entropy of black holes and discuss some applications of the formalism, in particular to the study of the thermodynamic limit. The main reason to look at this issue is the fact that the entropy must be a smooth function if one wants to remain within the confines of standard thermodynamics. Also, in precision studies of the entropy, it is important to check wether subdominant corrections for the statistical and the thermodynamical entropy coincide. |
Title: Inclusion of matter in inhomogeneous loop quantum cosmology. Authors: Daniel Martín-de Blas, Mercedes Martín-Benito, Guillermo A. Mena Marugán. Journal-ref: AIP Conf. Proc. 1458, 467 (2012). Abstract: We study the hybrid quantization of the linearly polarized Gowdy $T^3$ model with a massless scalar field with the same symmetries as the metric. For simplicity, we quantize its restriction to the model with local rotational symmetry. Using this hybrid approach, the homogeneous degrees of freedom of the geometry are quantized à la loop, leading to the resolution of the cosmological singularity. A Fock quantization is employed both for the matter and the gravitational inhomogeneities. Owing to the inclusion of the massless scalar field this system allows us to modelize flat Friedmann-Robertson-Walker cosmologies filled with inhomogeneities propagating in one direction, providing a perfect scenario to study the quantum back-reaction of the inhomogeneities on the polymeric homogeneous and isotropic background. |
Title: A complete hybrid quantization in inhomogeneous cosmology. Authors: Javier Olmedo, Mikel Fernández-Méndez, Guillermo A. Mena Marugán. Journal-ref: AIP Conf. Proc. 1458, 507 (2012). Abstract: A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on the minimum volume section, and from this we construct the physical Hilbert space. Moreover, a perturbative study allows us to introduce small inhomogeneities. After gauge fixing, the inhomogeneous part of the system is reduced to a linear field theory. We then adopt a standard Fock representation to quantize these degrees of freedom. For the considered case of compact spatial topology, the requirements of: i) invariance under the spatial isometries, and ii) unitary implementation of the quantum dynamics, pick up a unique Fock representation and a particular set of canonical fields (up to unitary equivalence). |
Title: Hybrid classical-quantum formulations ask for hybrid notions. Authors: Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay, Ricardo Gómez-Escalante. Journal-ref: Phys. Rev. A 86, 042120 (2012). Abstract: We reappraise some of the hybrid classical-quantum models proposed in the literature with the goal of retrieving some of their common characteristics. In particular, first, we analyze in detail the Peres-Terno argument regarding the inconsistency of hybrid quantizations of the Sudarshan type. We show that to accept such hybrid formalism entails the necessity of dealing with additional degrees of freedom beyond those in the straight complete quantization of the system. Second, we recover a similar enlargement of degrees of freedom in the so-called statistical hybrid models. Finally, we use Wigner's quantization of a simple model to illustrate how in hybrid systems the subsystems are never purely classical or quantum. A certain degree of quantumness (classicality) is being exchanged between the different sectors of the theory, which in this particular unphysical toy model makes them undistinguishable. |
Title: Geometry of fractional spaces. Authors: Gianluca Calcagni. Journal-ref: Adv. Theor. Math. Phys. 16, 549 (2012). Abstract: We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool is fractional calculus, which is cast in a way convenient for the definition of the differential structure, distances, volumes, and symmetries. By an extensive use of concepts and techniques of fractal geometry, we clarify the relation between fractional calculus and fractals, showing that fractional spaces can be regarded as fractals when the ratio of their Hausdorff and spectral dimension is greater than one. All the results are analytic and constitute the foundation for field theories living on multi-fractal spacetimes, which are presented in a companion paper. |
Title: Scalar perturbations from brane-world inflation with curvature effects. Authors: Mariam Bouhmadi-Lopez, Pisin Chen, Yen-Wei Liu. Journal-ref: Phys. Rev. A 86, 042120 (2012). Abstract: We consider a generalization of the Randall-Sundrum single brane-world scenario (RS2). More precisely, the generalization is described through curvature corrections, corresponding to a Gauss-Bonnet term in the bulk and a Hilbert-Einstein term, as well as the strength of the induced gravity term, on the brane. We are mainly interested in analyzing the early inflationary era of the brane, which we model within the extreme slow-roll limit, i.e., under a de Sitter like brane inflation, where the inflaton field is confined on the brane. We compute the scalar perturbations in this model and compare our results with those previously obtained for the RS2 scenario with and without an induced gravity term on the brane or a Gauss-Bonnet term in the bulk. The amplitude of the scalar perturbations is decreased as compared with a pure RS2 model. In addition, the effect from the Gauss-Bonnet correction in an induced gravity brane-world model is to decrease the amplitude of the scalar perturbations, and a similar result is obtained for the induced gravity effect in a Gauss-Bonnet brane-world. In general, in the high energy limit the amplitude is highly suppressed by the Gauss-Bonnet effect. Finally, we constrain the model using the latest WMAP7 data. |
Title: Diffusion in multiscale spacetimes. Authors: Gianluca Calcagni. Journal-ref: Phys. Rev. E 87, 012123 (2013). Abstract: We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are partly based on the literature in probability and percolation theory but their physical interpretation here is different since they apply to quantum spacetime itself. The case of multiscale (in particular, multifractal) spacetimes is then considered through a number of examples, and the most general spectral-dimension profile of multifractional spaces is constructed. |
Title: Hybrid quantization of an inflationary universe. Authors: Mikel Fernández-Méndez, Guillermo A. Mena Marugán, Javier Olmedo. Journal-ref: Phys. Rev. D 86, 024003 (2012). Abstract: We quantize to completion an inflationary universe with small inhomogeneities in the framework of loop quantum cosmology. The homogeneous setting consists of a massive scalar field propagating in a closed, homogeneous scenario. We provide a complete quantum description of the system employing loop quantization techniques. After introducing small inhomogeneities as scalar perturbations, we identify the true physical degrees of freedom by means of a partial gauge fixing, removing all the local degrees of freedom except the matter perturbations. We finally combine a Fock description for the inhomogeneities with the polymeric quantization of the homogeneous background, providing the quantum Hamiltonian constraint of the composed system. Its solutions are then completely characterized, owing to the suitable choice of quantum constraint, and the physical Hilbert space is constructed. Finally, we consider the analog description for an alternate gauge and, moreover, in terms of gauge- invariant quantities. In the deparametrized model, all these descriptions are unitarily equivalent at the quantum level. |
Title: The fate of non-trivial entanglement under gravitational collapse. Authors: Eduardo Martín-Martínez, Luis J. Garay, Juan León. Journal-ref: Class. Quantum Grav. 29: 224006 (2012). Abstract: We analyse the evolution of the entanglement of a non-trivial initial quantum field state (which, for simplicity, has been taken to be a bipartite state made out of vacuum and the first excited state) when it undergoes a gravitational collapse. We carry out this analysis by generalising the tools developed to study entanglement behaviour in stationary scenarios and making them suitable to deal with dynamical spacetimes. We also discuss what kind of problems can be tackled using the formalism spelled out here as well as single out future avenues of research. |
Title: Unique Fock quantization of scalar cosmological perturbations. Authors: Mikel Fernández-Méndez, Guillermo A. Mena Marugán, Javier Olmedo, José M. Velhinho. Journal-ref: Phys. Rev. D 85, 103525 (2012). Abstract: We investigate the ambiguities in the Fock quantization of the scalar perturbations of a Friedmann-Lemaître-Robertson-Walker model with a massive scalar field as matter content. We consider the case of compact spatial sections (thus avoiding infrared divergences), with the topology of a three-sphere. After expanding the perturbations in series of eigenfunctions of the Laplace-Beltrami operator, the Hamiltonian of the system is written up to quadratic order in them. We fix the gauge of the local degrees of freedom in two different ways, reaching in both cases the same qualitative results. A canonical transformation, which includes the scaling of the matter field perturbations by the scale factor of the geometry, is performed in order to arrive at a convenient formulation of the system. We then study the quantization of these perturbations in the classical background determined by the homogeneous variables. Based on previous work, we introduce a Fock representation for the perturbations in which: (a) the complex structure is invariant under the isometries of the spatial sections and (b) the field dynamics is implemented as a unitary operator. These two properties select not only a unique unitary equivalence class of representations, but also a preferred field description, picking up a canonical pair of field variables among all those that can be obtained by means of a time-dependent scaling of the matter field (completed into a linear canonical transformation). Finally, we present an equivalent quantization constructed in terms of gauge-invariant quantities. We prove that this quantization can be attained by a mode-by-mode time-dependent linear canonical transformation which admits a unitary implementation, so that it is also uniquely determined. |
Date: 27 Apr 2012
Subject: BH in LQG
Comments: Proceedings article
Title: Black hole entropy in loop quantum gravity. Authors: Iván Agulló, J. Fernando Barbero G., Enrique F. Borja, Jacobo Díaz-Polo, Eduardo J. S. Villaseñor. Journal-ref: J. Phys.: Conf. Ser. 360, 012035 (2012). Abstract: We discuss the recent progress on black hole entropy in loop quantum gravity, focusing in particular on the recently discovered discretization effect for microscopic black holes. Powerful analytical techniques have been developed to perform the exact computation of entropy. A statistical analysis of the structures responsible for this effect shows its progressive damping and eventual disappearance as one increases the considered horizon area. |
Date: 27 Apr 2012
Subject: Perturbations in LQC
Comments: Proceedings article
Title: Inflation and inhomogeneities: a hybrid quantization. Authors: Javier Olmedo, Mikel Fernández-Méndez, Guillermo A. Mena Marugán. Journal-ref: J. Phys.: Conf. Ser. 360, 012033 (2012). Abstract: We provide a complete quantization of a homogeneous and isotropic spacetime with positive spatial curvature coupled to a massive scalar field in the framework of Loop Quantum Cosmology. The physical Hilbert space is constructed out of the space of initial data on the minimum volume section. By means of a perturbative treatment we introduce inhomogeneities and thereafter we adopt a hybrid quantum approach, in which these inhomogeneous degrees of freedom are described by a standard Fock quantization. For the considered case of compact spatial topology, the requirements of: i) invariance of the vacuum state under the spatial isometries, and ii) unitary implementation of the quantum dynamics, pick up a privileged set of canonical fields and a unique Fock representation (up to unitary equivalence). |
Title: Inhomogenous loop quantum cosmology with matter. Authors: Daniel Martín-de Blas, Mercedes Martín-Benito, Guillermo A. Mena Marugán. Journal-ref: J. Phys.: Conf. Ser. 360, 012032 (2012). Abstract: The linearly polarized Gowdy $T^3$ model with a massless scalar field with the same symmetries as the metric is quantized by applying a hybrid approach. The homogeneous geometry degrees of freedom are loop quantized, fact which leads to the resolution of the cosmological singularity, while a Fock quantization is employed for both matter and gravitational inhomogeneities. Owing to the inclusion of the massless scalar field this system allows us to modelize flat Friedmann-Robertson-Walker cosmologies filled with inhomogeneities propagating in one direction. It provides a perfect scenario to study the quantum back-reaction between the inhomogeneities and the polymeric homogeneous and isotropic background. |
Title: Hawking radiation as perceived by different observers. Authors: Luis C. Barbado, Carlos Barceló, Luis J. Garay. Journal-ref: AIP Conf. Proc. 1458, 363 (2012). Abstract: We study the perception of Hawking radiation by different observers outside a black hole. The analysis is done in terms of an effective-temperature function that varies along the trajectory of each observer. The vacuum state of the radiation field is chosen to be non-stationary, so as to mimic the switching-on of Hawking radiation that would appear in a real black hole collapse. We analyse how this vacuum is perceived by observers staying at a fixed radius, by observers coming in free-fall from radial infinity at different times, and by observers in free-fall released from finite radial positions. Results found have a compelling physical interpretation. One main result, at first unexpected, is that in general free-falling observers do perceive particle emission by the black hole when crossing the event horizon. This happens because of a diverging Doppler shift at the event horizon. |
Title: Unique Fock quantization of scalar cosmological perturbations. Authors: Thiago S. Pereira, Saulo Carneiro, Guillermo A. Mena Marugán. Journal-ref: JCAP 05 (2012) 040. Abstract: In this work, the linear and gauge-invariant theory of cosmological perturbations in a class of anisotropic and shear-free spacetimes is developed. After constructing an explicit set of complete eigenfunctions in terms of which perturbations can be expanded, we identify the effective degrees of freedom during a generic slow-roll inflationary phase. These correspond to the anisotropic equivalent of the standard Mukhanov-Sasaki variables. The associated equations of motion present a remarkable resemblance to those found in perturbed Friedmann-Robertson-Walker spacetimes with curvature, apart from the spectrum of the Laplacian, which exhibits the characteristic frequencies of the underlying geometry. In particular, it is found that the perturbations cannot develop arbitrarily large super-Hubble modes. |
Title: Criteria for the determination of time dependent scalings in the Fock quantization of scalar fields with a time dependent mass in ultrastatic spacetimes. Authors: Jerónimo Cortez, Guillermo A. Mena Marugán, Javier Olmedo, José M. Velhinho. Journal-ref: Phys. Rev. D 86, 104003 (2012). Abstract: For Klein-Gordon fields, it is well known that there exist an infinite number of nonequivalent Fock representations of the canonical commutation relations and, therefore, of inequivalent quantum theories. A context in which this kind of ambiguities arises and prevents the derivation of robust results is, e.g., in the quantum analysis of cosmological perturbations. In these situations, typically, a suitable scaling of the field by a time dependent function leads to a description in an auxiliary static background, though the nonstationarity still shows up in a time dependent mass. For such a field description, and assuming the compactness of the spatial sections, we recently proved in three or less spatial dimensions that the criteria of a natural implementation of the spatial symmetries and of a unitary time evolution are able to select a unique class of unitarily equivalent vacua, and hence of Fock representations. In this work, we succeed to extend our uniqueness result to the consideration of all possible field descriptions that can be reached by a time dependent canonical transformation which, in particular, involves a scaling of the field by a function of time. This kind of canonical transformations modify the dynamics of the system and introduce a further ambiguity in its quantum description, exceeding the choice of a Fock representation. Remarkably, for any compact spatial manifold in less than four dimensions, we show that our criteria eliminate any possible nontrivial scaling of the field other than that leading to the description in an auxiliary static background. Besides, we show that either no time dependent redefinition of the field momentum is allowed or, if this may happen, the redefinition does not introduce any Fock representation that cannot be obtained by a unitary transformation. |
Title: Prime numbers, quantum field theory and the Goldbach conjecture. Authors: Miguel-Angel Sanchis-Lozano, J. Fernando Barbero G., Jose Navarro-Salas. Journal-ref: Int. J. Mod. Phys. A 27, 1250136 (2012). Abstract: Motivated by the Goldbach and Polignac conjectures in Number Theory, we propose the factorization of a classical non-interacting real scalar field (on a two-cylindrical spacetime) as a product of either two or three (so-called primer) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such primer fields and construct the corresponding Fock space by introducing creation operators $a_p^{\dag}$ (labeled by prime numbers $p$) acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory, suggests intriguing connections between different topics in Number Theory, notably the Riemann hypothesis and the Goldbach and Polignac conjectures. Our analysis also suggests that the (non) renormalizability properties of the proposed model could be linked to the possible validity or breakdown of the Goldbach conjecture for large integer numbers. |
Title: Hawking radiation as perceived by different observers: An analytic expression for the effective-temperature function. Authors: Luis C. Barbado, Carlos Barceló, Luis J. Garay. Journal-ref: Class. Quant. Grav. 29: 075013 (2012). Abstract: Given a field vacuum state in a black hole spacetime, this state can be analyzed in terms of how it is perceived (in terms of particle content) by different observers. This can be done by means of the effective-temperature function introduced by Barcel\'o et al. in [1]. In Barbado et al. [2], this function was analyzed in a case by case basis for a number of interesting situations. In this work, we find a general analytic expression for the effective-temperature function which, apart from the vacuum state choice, depends on the position, the local velocity and the acceleration of the specific observer. We give a clear physical interpretation of the quantities appearing in the expression, and we illustrate its potentiality with a few examples. |
Title: Two formalisms, one renormalized stress-energy tensor. Authors: Carlos Barceló, Raúl Carballo, Luis J. Garay. Journal-ref: Phys. Rev. D 85, 084001 (2012). Abstract: We explicitly compare the structure of the renormalized stress-energy tensor (RSET) of a massless scalar field in a (1+1) curved spacetime as obtained by two different renormalization methods: point splitting and one-loop effective action. We pay special attention to where and how it is encoded the information related to the choice of vacuum state in both formalisms. By establishing a clear translation map between both procedures, we show that these two potentially different RSET are actually equal, when using vacuum-state choices related by this map. One specific aim of the analysis is to facilitate the comparison of results regarding semiclassical effects in gravitational collapse as obtained within these different formalisms. |
Title: Loop quantum cosmology of the Bianchi I model: complete quantization. Authors: M Martín-Benito, L J Garay, G A Mena Marugán, E. Wilson-Ewing. Journal-ref: Journal of Physics: Conference Series 360, 012031 (2012) Abstract: We complete the canonical quantization of the vacuum Bianchi I model within the improved dynamics scheme of loop quantum cosmology, characterizing the Hilbert structure of the physical states and providing a complete set of observables acting on them. In order to achieve this task, it has been essential to determine the structure of the separable superselection sectors that arise owing to the polymeric quantization, and to prove that the initial value problem obtained when regarding the Hamiltonian constraint as an evolution equation, interpreting the volume as the evolution parameter, is well-posed. |
Title: The trans-Planckian problem as a guiding principle. Authors: Luis C. Barbado, Carlos Barceló, Luis J. Garay, Gil Jannes. Journal-ref: JHEP 11, 112 (2011) Abstract: We use the avoidance of the trans-Planckian problem of Hawking radiation as a guiding principle in searching for a compelling scenario for the evaporation of black holes or black-hole-like objects. We argue that there exist only three possible scenarios, depending on whether the classical notion of long-lived horizon is preserved by high-energy physics and on whether the dark and compact astrophysical objects that we observe have long-lived horizons in the first place. Along the way, we find that (i) a theory with high-energy superluminal signalling and a long-lived trapping horizon would be extremely unstable in astrophysical terms and that (ii) stellar pulsations of objects hovering right outside but extremely close to their gravitational radius can result in a mechanism for Hawking-like emission. |
Title: Prescriptions in Loop Quantum Cosmology: A comparative analysis. Authors: Guillermo A. Mena Marugan, Javier Olmedo, Tomasz Pawlowski. Journal-ref: Phys. Rev. D 84, 064012 (2011). Abstract: Various prescriptions proposed in the literature to attain the polymeric quantization of a homogeneous and isotropic flat spacetime coupled to a massless scalar field are carefully analyzed in order to discuss their differences. A detailed numerical analysis confirms that, for states which are not deep in the quantum realm, the expectation values and dispersions of some natural observables of interest in cosmology are qualitatively the same for all the considered prescriptions. On the contrary, the amplitude of the wave functions of those states differs considerably at the bounce epoch for these prescriptions. This difference cannot be absorbed by a change of representation. Finally, the prescriptions with simpler superselection sectors are clearly more efficient from the numerical point of view. |
Date: 2 Aug 2011
Subject: BH in LQG.
Comments: Proceedings article
Title: Black hole entropy: lessons from loop quantum gravity. Authors: J Fernando Barbero G. Journal-ref: Journal of Physics: Conference Series 314, 012003 (2011). Abstract: The purpose of this contribution is is to discuss black hole entropy in the loop quantum gravity framework. Special attention is paid to the description of the microscopic degrees of freedom responsible for the entropy, the statement of the combinatorial problems that must be solved in order to count them, and the behaviour of the entropy as a function of the horizon area. In particular I will review the derivation of the Bekenstein-Hawking law and its logarithmic corrections. I end with a comparison between the results derived within loop quantum gravity and the ones obtained by other approaches. |
Date: 2 Aug 2011
Subject: LQC.
Comments: Proceedings article
Title: Further improvements in the understanding of LQC. Authors: J. Olmedo, M. Martín Benito and G. A. Mena Marugán. Journal-ref: Journal of Physics: Conference Series 314, 012048 (2011). Abstract: Loop Quantum Cosmology provides a successful quantization of isotropic and homogeneous flat universes with a massless, homogeneous scalar field as the matter content. Here, we propose a new ordering for the Hamiltonian constraint operator that facilitates the quantization of this model and makes the physical consequences much more transparent. In particular, our constraint is such that, in the gravitational sector, the zero volume state decouples, allowing us to get rid of the cosmological singularity already at a kinematical level, as well as to introduce a consistent densitization procedure for the constraint. Furthermore, the typical discretization of the spatial volume is achieved in superselection sectors which prove to be most suitable, with support on semilattices and where the basic functions that codify all the relevant information about the geometry have the expected Wheeler-DeWitt limit of standing waves. Thanks to these properties, we can demonstrate that the quantum bounce is generic for any physical state and superselection sector. |
Title: A uniqueness criterion for the Fock quantization of scalar fields with time dependent mass. Authors: Jeronimo Cortez, Guillermo A. Mena Marugan, Javier Olmedo, Jose M. Velhinho. Journal-ref: Class. Quantum Grav. 28: 172001 (2011) Abstract: A major problem in the quantization of fields in curved spacetimes is the ambiguity in the choice of a Fock representation for the canonical commutation relations. There exists an infinite number of choices leading to different physical predictions. In stationary scenarios, a common strategy is to select a vacuum (or a family of unitarily equivalent vacua) by requiring invariance under the spacetime symmetries. When stationarity is lost, a natural generalization consists in replacing time invariance by unitarity in the evolution. We prove that, when the spatial sections are compact, the criterion of a unitary dynamics, together with the invariance under the spatial isometries, suffices to select a unique family of Fock quantizations for a scalar field with time dependent mass. |
Title: Effective dynamics of the hybrid quantization of the Gowdy T^{3} universe. Authors: David Brizuela, Guillermo A. Mena Marugan, Tomasz Pawlowski. Journal-ref: Physical Review D 84, 124017 (2011) Abstract: The quantum dynamics of the linearly polarized Gowdy T^3 model (compact inhomogeneous universes admitting linearly polarized gravitational waves) is analyzed within Loop Quantum Cosmology by means of an effective dynamics. The analysis, performed via analytical and numerical methods, proves that the behavior found in the evolution of vacuum (homogeneous) Bianchi I universes is preserved qualitatively also in the presence of inhomogeneities. More precisely, the initial singularity is replaced by a big bounce which joins deterministically two large classical universes. In addition, we show that the size of the universe at the bounce is at least of the same order of magnitude (roughly speaking) as the size of the corresponding homogeneous universe obtained in the absence of gravitational waves. In particular, a precise lower bound for the ratio of these two sizes is found. Finally, the comparison of the amplitudes of the gravitational wave modes in the distant future and past shows that, statistically (i.e., for large samples of universes), the difference in amplitude is enhanced for nearly homogeneous universes, whereas this difference vanishes in inhomogeneity dominated cases. The presented analysis constitutes the first systematic effective study of an inhomogeneous system within Loop Quantum Cosmology, and it proves the robustness of the results obtained for homogeneous cosmologies in this context. |
Title: The thermodynamic limit and black hole entropy in the area ensemble. Authors: J. Fernando Barbero G., Eduardo J. S. Villaseñor. Journal-ref: Class. Quant. Grav. 28: 215014 (2011) Abstract: We discuss the thermodynamic limit in the canonical area ensemble used in loop quantum gravity to model quantum black holes. The computation of the thermodynamic limit is the rigorous way to obtain a smooth entropy from the counting entropy given by a direct determination of the number of microstates compatible with macroscopic quantities (the energy in standard statistical mechanics or the area in the framework presented here). As we will show in specific examples the leading behavior of the smoothed entropy for large horizon areas is the same as the counting entropy but the subleading contributions differ. This is important because these corrections determine the concavity or convexity of the entropy as a function of the area. |
Title: Hawking radiation as perceived by different observers. Authors: Luis C. Barbado, Carlos Barceló, Luis J. Garay. Journal-ref: Class. Quant. Grav. 28: 125021 (2011) Abstract: We use a method recently introduced in Barceló et al, arXiv:1011.5593 [gr-qc] to analyse Hawking radiation in a Schwarzschild black hole as perceived by different observers in the system. The method is based on the introduction of an "effective temperature" function that varies with time. First we introduce a non-stationary vacuum state for a quantum scalar field, which interpolates between the Boulware vacuum state at early times and the Unruh vacuum state at late times. In this way we mimic the process of switching on Hawking radiation in realistic collapse scenarios. Then, we analyse this vacuum state from the perspective of static observers at different radial positions, observers undergoing a free-fall trajectory from infinity, and observers standing at rest at a radial distance and then released to fall freely towards the horizon. The physical image that emerges from these analyses is rather rich and compelling. Among many other results, we find that generic freely-falling observes do not perceive vacuum when crossing the horizon, but an effective temperature a few times larger than the one that they perceived when started to free-fall. We explain this phenomenon as due to a diverging Doppler effect at horizon crossing. |
Title: Statistical description of the black hole degeneracy spectrum. Authors: J. Fernando Barbero G., Eduardo J. S. Villaseñor. Journal-ref: Phys. Rev. D 83: 104013 (2011) Abstract: We use mathematical methods based on generating functions to study the statistical properties of the black hole degeneracy spectrum in loop quantum gravity. In particular we will study the persistence of the observed effective quantization of the entropy as a function of the horizon area. We will show that this quantization disappears as the area increases despite the existence of black hole configurations with a large degeneracy. The methods that we describe here can be adapted to the study of the statistical properties of the black hole degeneracy spectrum for all the existing proposals to define black hole entropy in loop quantum gravity. |
Title: Detailed black hole state counting in loop quantum gravity. Authors: Ivan Agullo, J. Fernando Barbero G., Enrique F. Borja, Jacobo Diaz-Polo, Eduardo J. S. Villaseñor. Journal-ref: Phys. Rev. D 82, 084029 (2010) Abstract: We give a complete and detailed description of the computation of black hole entropy in loop quantum gravity by employing the most recently introduced number-theoretic and combinatorial methods. The use of these techniques allows us to perform a detailed analysis of the precise structure of the entropy spectrum for small black holes, showing some relevant features that were not discernible in previous computations. The ability to manipulate and understand the spectrum up to the level of detail that we describe in the paper is a crucial step toward obtaining the behavior of entropy in the asymptotic (large horizon area) regime. |
Title: Uniqueness of the Fock quantization of fields with unitary dynamics in nonstationary spacetimes. Authors: Jeronimo Cortez, Guillermo A. Mena Marugan, Javier Olmedo, Jose M. Velhinho. Journal-ref: Phys. Rev. D 83, 025002 (2011) Abstract: The Fock quantization of fields propagating in cosmological spacetimes is not uniquely determined because of several reasons. Apart from the ambiguity in the choice of the quantum representation of the canonical commutation relations, there also exists a certain freedom in the choice of field: one can scale it arbitrarily absorbing background functions, which are spatially homogeneous but depend on time. Each nontrivial scaling turns out into a different dynamics and, in general, into an inequivalent quantum field theory. In this work we analyze this freedom at the quantum level for a scalar field in a nonstationary, homogeneous spacetime whose spatial sections have S^{3} topology. A scaling of the configuration variable is introduced as part of a linear, time dependent canonical transformation in phase space. In this context, we prove in full detail a uniqueness result about the Fock quantization requiring that the dynamics be unitary and the spatial symmetries of the field equations have a natural unitary implementation. The main conclusion is that, with those requirements, only one particular canonical transformation is allowed, and thus only one choice of the field-momentum pair (up to irrelevant constant scalings). This complements another previous uniqueness result for scalar fields with a time varying mass on S^{3}, which selects a specific equivalence class of Fock representations of the canonical commutation relations under the conditions of a unitary evolution and the invariance of the vacuum under the background symmetries. In total, the combination of these two different statements of uniqueness picks up a unique Fock quantization for the system. We also extend our proof of uniqueness to other compact topologies and spacetime dimensions. |
Title: Loop Quantum Cosmology: A cosmological theory with a view. Authors: Guillermo A. Mena Marugan. Journal-ref: Journal of Physics: Conference Series 314, 012012 (2011) Abstract: Loop Quantum Gravity is a background independent, nonperturbative approach to the quantization of General Relativity. Its application to models of interest in cosmology and astrophysics, known as Loop Quantum Cosmology, has led to new and exciting views of the gravitational phenomena that took place in the early universe, or that occur in spacetime regions where Einstein's theory predicts singularities. We provide a brief introduction to the bases of Loop Quantum Cosmology and summarize the most important results obtained in homogeneous scenarios. These results include a mechanism to avoid the cosmological Big Bang singularity and replace it with a Big Bounce, as well as the existence of processes which favor inflation. We also discuss the extension of the frame of Loop Quantum Cosmology to inhomogeneous settings. |
Title: Quantum Gowdy model within the new loop quantum cosmology improved dynamics. Authors: Mercedes Martín-Benito, Luis J. Garay, Guillermo A. Mena Marugán. Journal-ref: Journal of Physics: Conference Series 314, 012047 (2011) Abstract: The linearly polarized Gowdy T^{3} model can be regarded as compact Bianchi I cosmologies with inhomogeneous modes allowed to travel in one direction. We study a hybrid quantization of this model that combines the loop quantization of the Bianchi I background, adopting the improved dynamics scheme put forward by Ashtekar and Wilson-Ewing, with a Fock quantization for the inhomogeneities. The Hamiltonian constraint operator provides a resolution of the cosmological singularity and superselects separable sectors. We analyze the complicated structure of these sectors. In any of them the Hamiltonian constraint provides an evolution equation with respect to the volume of the associated Bianchi I universe, with a well posed initial value problem. This fact allows us to construct the Hilbert space of physical states and to show that we recover the standard quantum field theory for the inhomogeneities. |
Title: Matter in inhomogeneous loop quantum cosmology: the Gowdy T^{3} model. Authors: Mercedes Martín-Benito, Daniel Martín-de Blas, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D83: 084050 (2011) Abstract: We apply a hybrid approach which combines loop and Fock quantizations to fully quantize the linearly polarized Gowdy T^{3} model in the presence of a massless scalar field with the same symmetries as the metric. Like in the absence of matter content, the application of loop techniques leads to a quantum resolution of the classical cosmological singularity. Most importantly, thanks to the inclusion of matter, the homogeneous sector of the model contains flat Friedmann-Robertson-Walker (FRW) solutions, which are not allowed in vacuo. Therefore, this model provides a simple setting to study at the quantum level interesting physical phenomena such as the effect of the anisotropies and inhomogeneities on flat FRW cosmologies. |
Title: Acceleration radiation, transition probabilities, and trans-Planckian physics. Authors: I. Agullo, J. Navarro-Salas, G. J. Olmo, L. Parker. Journal-ref: New J.Phys.12: 095017 (2010) Abstract: An important question in the derivation of the acceleration radiation, which also arises in Hawking's derivation of black hole radiance, is the need to invoke trans-Planckian physics in describing the creation of quanta. We point out that this issue can be further clarified by reconsidering the analysis in terms of particle detectors, transition probabilities and local two-point functions. By writing down separate expressions for the spontaneous- and induced-transition probabilities of a uniformly accelerated detector, we show that the bulk of the effect comes from the natural (non-trans-Planckian) scale of the problem, which largely diminishes the importance of the trans-Planckian sector. This is so, at least, when trans-Planckian physics is defined in a Lorentz-invariant way. This analysis also suggests how one can define and estimate the role of trans-Planckian physics in the Hawking effect itself. |
Title: Quantization of Midisuperspace Models. Authors: J. Fernando Barbero G., Eduardo J. S. Villaseñor. Journal-ref: Living Rev. Rel.13: 6 (2010) Abstract: We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop quantum gravity inspired methods. |
Title: Quantum entanglement produced in the formation of a black hole. Authors: Eduardo Martín-Martinez, Luis J. Garay, Juan León. Journal-ref: Phys. Rev. D 82: 064028 (2010) Abstract: We analyze the entanglement degradation provoked by the Hawking effect in a bipartite system Alice-Rob when Rob is in the proximities of a Schwarzschild black hole while Alice is free falling into it. We will obtain the limit in which the tools imported from the Unruh entanglement degradation phenomenon can be used properly, keeping control on the approximation. As a result, we will be able to determine the degree of entanglement as a function of the distance of Rob to the event horizon, the mass of the black hole, and the frequency of Rob's entangled modes. By means of this analysis we will show that all the interesting phenomena occur in the vicinity of the event horizon and that the presence of event horizons do not effectively degrade the entanglement when Rob is far off the black hole. The universality of the phenomenon is presented: There are not fundamental differences for different masses when working in the natural unit system adapted to each black hole. We also discuss some aspects of the localization of Alice and Rob states. All this study is done without using the single mode approximation. |
Title: Hawking radiation by Kerr black holes and conformal symmetry. Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker. Journal-ref: Phys.Rev.Lett.105: 211305 (2010) Abstract: The exponential blueshift associated with the event horizon of a black hole makes conformal symmetry play a fundamental role in accounting for its thermal properties. Using a derivation based on two-point functions, we show that the full spectrum of thermal radiation of scalar particles by Kerr black holes can be explicitly derived on the basis of a conformal symmetry arising in the wave equation near the horizon. The simplicity of our approach emphasizes the depth of the connection between conformal symmetry and black hole radiance. |
Title: Hybrid Quantization: From Bianchi I to the Gowdy Model. Authors: Mercedes Martín-Benito, Guillermo A. Mena Marugán, Edward Wilson-Ewing. Journal-ref: Phys. Rev. D 82: 084012 (2010) Abstract: We complete the quantization of the vacuum Bianchi I model within the framework of loop quantum cosmology adopting a new improved dynamics scheme put forward recently. In addition, we revisit the hybrid quantization of the Gowdy T3 cosmologies with linear polarization using that scheme, proving with rigor some steps that remained unconcluded. The family of Gowdy T3 cosmologies is an inhomogeneous model whose subset of homogeneous solutions is given precisely by the vacuum Bianchi I model. Our hybrid approach combines the new loop quantum cosmology description of this homogeneous sector with a Fock quantization of the inhomogeneities. Both in the Bianchi I model and in the Gowdy model the Hamiltonian constraint provides an evolution equation with respect to the volume of the Bianchi I universe, which is a discrete variable with a strictly positive minimum. We show that, in vacuo, this evolution is well defined inasmuch as the associated initial value problem is well posed: physical solutions are completely determined by the data on the initial section of constant Bianchi I volume. This fact allows us first to carry out to completion the quantization of the vacuum Bianchi I model which had not yet been achieved and then to confirm the feasibility of the hybrid procedure when the homogeneous sector is quantized with the new improved dynamics scheme. |
Title: Unveiling quantum entanglement degradation near a Schwarzschild black hole. Authors: Eduardo Martín-Martinez, Luis J. Garay, Juan León. Journal-ref: Phys. Rev. D 82: 064006 (2010) Abstract: We analyze the entanglement degradation provoked by the Hawking effect in a bipartite system Alice-Rob when Rob is in the proximities of a Schwarzschild black hole while Alice is free falling into it. We will obtain the limit in which the tools imported from the Unruh entanglement degradation phenomenon can be used properly, keeping control on the approximation. As a result, we will be able to determine the degree of entanglement as a function of the distance of Rob to the event horizon, the mass of the black hole, and the frequency of Rob's entangled modes. By means of this analysis we will show that all the interesting phenomena occur in the vicinity of the event horizon and that the presence of event horizons do not effectively degrade the entanglement when Rob is far off the black hole. The universality of the phenomenon is presented: There are not fundamental differences for different masses when working in the natural unit system adapted to each black hole. We also discuss some aspects of the localization of Alice and Rob states. All this study is done without using the single mode approximation. |
Title: The two faces of quantum sound. Authors: C. Barcelo, L.J. Garay, G. Jannes. Journal-ref: Phys. Rev. D 82: 044042 (2010) Abstract: Fluctuations around a Bose-Einstein condensate can be described by means of Bogolubov theory leading to the notion of quasiparticle and antiquasiparticle familiar to nonrelativistic condensed-matter practitioners. On the other hand, we already know that these perturbations evolve according to a relativistic Klein-Gordon equation in the long-wavelength approximation. For shorter wavelengths, we show that this equation acquires nontrivial corrections which modify the Klein-Gordon product. In this approach, quasiparticles can also be defined (up to the standard ambiguities due to observer dependence). We demonstrate that—in the low-energy as well as in the high-energy regimes—both concepts of quasiparticle are actually the same, regardless of the formalism (Bogolubov or Klein-Gordon) used to describe them. These results also apply to any barotropic, inviscid, irrotational fluid, with or without quantum potential. Finally, we illustrate how the quantization of these systems of quasiparticles proceeds by analyzing a stationary configuration containing an acoustic horizon. We show that there are several possible choices of a regular vacuum state, including a regular generalization of the Boulware vacuum. Issues such us Hawking radiation crucially depend on this vacuum choice. |
Title: Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization of the Gowdy Model. Authors: L.J. Garay, M. Martín-Benito, G.A. Mena Marugán. Journal-ref: Phys. Rev. D 82: 044048 (2010) Abstract: The Gowdy cosmologies provide a suitable arena to further develop loop quantum cosmology, allowing the presence of inhomogeneities. For the particular case of Gowdy spacetimes with the spatial topology of a three-torus and a content of linearly polarized gravitational waves, we detail a hybrid quantum theory in which we combine a loop quantization of the degrees of freedom that parametrize the subfamily of homogeneous solutions, which represent Bianchi I spacetimes, and a Fock quantization of the inhomogeneities. Two different theories are constructed and compared, corresponding to two different schemes for the quantization of the Bianchi I model within the improved dynamics formalism of loop quantum cosmology. One of these schemes has been recently put forward by Ashtekar and Wilson-Ewing. We address several issues, including the quantum resolution of the cosmological singularity, the structure of the superselection sectors in the quantum system, or the construction of the Hilbert space of physical states. |
Title: Isotropic and Anisotropic Bouncing Cosmologies in Palatini Gravity. Authors: Carlos Barragan, Gonzalo J. Olmo. Journal-ref: Phys. Rev. D 82: 084015 (2010) Abstract: We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini f(R) and f(R,RμνRμν) theories of gravity with a perfect fluid and consider the existence of nonsingular bouncing solutions in the early universe. We find that all f(R) models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model R+aR2/RP+RμνRμν/RP exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for a < 0) and radiation (for arbitrary a). It thus represents a purely gravitational solution to the big bang singularity and anisotropy problems of general relativity without the need for exotic (w>1) sources of matter/energy or extra degrees of freedom. |
arXives: 1005.2727
Date: 16 May 2010
Subject: QFT in curved spaces, Inflation.
Comments: Proceedings article
Title: Reply to "Comment on 'Insensitivity of Hawking radiation to an invariant Planck-scale cutoff'". Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker. Journal-ref: Phys. Rev. D 81: 108502 (2010) Abstract: We clarify the relationship between the conclusions of the previous Comment of A. Helfer [A. Helfer, preceding Comment, Phys. Rev. D 81, 108501 (2010)] and that of our Brief Report [I. Agulló, J. Navarro-Salas, G. J. Olmo, and L. Parker, Phys. Rev. D 80, 047503 (2009).]. |
Title: A unique Fock quantization for fields in non-stationary spacetimes. Authors: Jeronimo Cortez, Guillermo A. Mena Marugan, Javier Olmedo, Jose M. Velhinho. Journal-ref: JCAP 1010: 030 (2010) Abstract: In curved spacetimes, the lack of criteria for the construction of a unique quantization is a fundamental problem undermining the significance of the predictions of quantum field theory. Inequivalent quantizations lead to different physics. Recently, however, some uniqueness results have been obtained for fields in non-stationary settings. In particular, for vacua that are invariant under the background symmetries, a unitary implementation of the classical evolution suffices to pick up a unique Fock quantization in the case of Klein-Gordon fields with time-dependent mass, propagating in a static spacetime whose spatial sections are three-spheres. In fact, the field equation can be reinterpreted as describing the propagation in a Friedmann-Robertson-Walker spacetime after a suitable scaling of the field by a function of time. For this class of fields, we prove here an even stronger result about the Fock quantization: the uniqueness persists when one allows for linear time-dependent transformations of the field in order to account for a scaling by background functions. In total, paying attention to the dynamics, there exists a preferred choice of quantum field, and only one SO(4)-invariant Fock representation for it that respects the standard probabilistic interpretation along the evolution. The result has relevant implications e.g. in cosmology. |
Title: Quantum Non-Gravity and Stellar Collapse. Authors: Carlos Barcelo, Luis J. Garay, Gil Jannes. Journal-ref: Found. Phys. 41: 1532-1541, 2011 Abstract: Observational indications combined with analyses of analogue and emergent gravity in condensed matter systems support the possibility that there might be two distinct energy scales related to quantum gravity: the scale that sets the onset of quantum gravitational effects E_{B} (related to the Planck scale) and the much higher scale E_{L} signalling the breaking of Lorentz symmetry. We suggest a natural interpretation for these two scales: E_{L} is the energy scale below which a special relativistic spacetime emerges, E_{B} is the scale below which this spacetime geometry becomes curved. This implies that the first `quantum' gravitational effect around E_{B} could simply be that gravity is progressively switched off, leaving an effective Minkowski quantum field theory up to much higher energies of the order of E_{L}. This scenario may have important consequences for gravitational collapse, inasmuch as it opens up new possibilities for the final state of stellar collapse other than an evaporating black hole. |
Title: Cosmic recall and the scattering picture of Loop Quantum Cosmology. Authors: Wojciech Kaminski, Tomasz Pawlowski. Journal-ref: Phys. Rev. D 81: 084027 (2010) Abstract: The global dynamics of a homogeneous universe in Loop Quantum Cosmology is viewed as a scattering process of its geometrodynamical equivalent. This picture is applied to build a flexible (easy to generalize) and not restricted just to exactly solvable models method of verifying the preservation of the semiclassicality through the bounce. The devised method is next applied to two simple examples: (i) the isotropic Friedman Robertson Walker universe, and (ii) the isotropic sector of the Bianchi I model. For both of them we show, that the dispersions in the logarithm of the volume ln(v) and scalar field momentum ln(p_phi) in the distant future and past are related via strong triangle inequalities. This implies in particular a strict preservation of the semiclassicality (in considered degrees of freedom) in both the cases (i) and (ii). Derived inequalities are general: valid for all the physical states within the considered models. |
Title: Fock quantization of a scalar field with time dependent mass on the three-sphere: unitarity and uniqueness. Authors: Jeronimo Cortez, Guillermo A. Mena Marugan, Jose M. Velhinho. Journal-ref: Phys. Rev. D 81: 044037 (2010) Abstract: We study the Fock description of a quantum free field on the three-sphere with a mass that depends explicitly on time, also interpretable as an explicitly time dependent quadratic potential. We show that, under quite mild restrictions on the time dependence of the mass, the specific Fock representation of the canonical commutation relations which is naturally associated with a massless free field provides a unitary dynamics even when the time varying mass is present. Moreover, we demonstrate that this Fock representation is the only acceptable one, up to unitary equivalence, if the vacuum has to be SO(4)-invariant (i.e., invariant under the symmetries of the field equation) and the dynamics is required to be unitary. In particular, the analysis and uniqueness of the quantization can be applied to the treatment of cosmological perturbations around Friedmann-Robertson-Walker spacetimes with the spatial topology of the three-sphere, like e.g. for gravitational waves (tensor perturbations). In addition, we analyze the extension of our results to free fields with a time dependent mass defined on other compact spatial manifolds. We prove the uniqueness of the Fock representation in the case of a two-sphere as well, and discuss the case of a three-torus. |
Title: The LQC evolution operator of FRW universe with positive cosmological constant. Authors: Wojciech Kaminski, Tomasz Pawlowski. Journal-ref: Phys. Rev. D81: 024014 (2010) Abstract: The self-adjointness of an evolution operator $\Theta_{\Lambda}$ corresponding to the model of flat FRW universe with massless scalar field and cosmological constant quantized in the framework of Loop Quantum Cosmology is studied in the case $\Lambda>0$. It is shown, that for $\Lambda < \Lambda_c\approx 10.3\,l_{Pl}^{-2}$ the operator admits many self-adjoint extensions, each of the purely discrete spectrum. On the other hand for $\Lambda\geq\Lambda_c$ the operator is essentially self-adjoint, however the physical Hilbert space of the model does not contain any physically interesting states. |
arXives: 0911.0961
Date: 5 Nov. 2009
Subject: QFT in curved space, Inflation.
Comments: Reg. article
Title: Revising the observable consequences of slow-roll inflation. Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker. Journal-ref: Phys.Rev.D81: 043514 (2010) Abstract: We study the generation of primordial perturbations in a (single-field) slow-roll inflationary universe. In momentum space, these (Gaussian) perturbations are characterized by a zero mean and a non-zero variance D^{2}(k, t). However, in position space the variance diverges in the ultraviolet. The requirement of a finite variance in position space forces one to regularize D^{2}(k, t). This can (and should) be achieved by proper renormalization in an expanding universe in a unique way. This affects the predicted scalar and tensorial power spectra (evaluated when the modes acquire classical properties) for wavelengths that today are at observable scales. As a consequence, the imprint of slow-roll inflation on the CMB anisotropies is significantly altered. We find a non-trivial change in the consistency condition that relates the tensor-to-scalar ratio r to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, n_{t}=0, is now compatible with a non-zero ratio $r\approx 0.12\pm0.06$, which is forbidden by the standard prediction (r=-8n_{t}). The influence of relic gravitational waves on the CMB may soon come within the range of planned measurements, offering a non-trivial test of the new predictions. |
Title: Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology. Authors: Mercedes Martin-Benito, Guillermo A. Mena Marugan, Javier Olmedo. Journal-ref: Physical Review D 80, 104015 (2009) Abstract: The flat, homogeneous, and isotropic universe with a massless scalar field is a paradigmatic model in Loop Quantum Cosmology. In spite of the prominent role that the model has played in the development of this branch of physics, there still remain some aspects of its quantization which deserve a more detailed discussion. These aspects include the kinematical resolution of the cosmological singularity, the precise relation between the solutions of the densitized and non-densitized versions of the quantum Hamiltonian constraint, the possibility of identifying superselection sectors which are as simple as possible, and a clear comprehension of the Wheeler-DeWitt (WDW) limit associated with the theory in those sectors. We propose an alternative operator to represent the Hamiltonian constraint which is specially suitable to deal with these issues in a satisfactory way. In particular, with our constraint operator, the singularity decouples in the kinematical Hilbert space and can be removed already at this level. Thanks to this fact, we can densitize the quantum Hamiltonian constraint in a rigorous manner. Besides, together with the physical observables, this constraint superselects simple sectors for the universe volume, with a support contained in a single semiaxis of the real line and for which the basic functions that encode the information about the geometry possess optimal physical properties. Namely, they provide a no-boundary description around the cosmological singularity and admit a well-defined WDW limit in terms of standing waves. Both properties explain the presence of a generic quantum bounce replacing the singularity at a fundamental level, in contrast with previous studies where the bounce was proved in concrete regimes and focusing on states with a marked semiclassical behavior. |
arXives: No entry
Date: 15 Jul 2009
Subject: Inflation
Comments: Essay Awarded by the Gravity Research Foundation
Title: Inflation, quantum fields, and CMB anisotropies. Authors: I.Agulló, J.Navarro-Salas, Gonzalo J. Olmo, Leonard Parker. Journal-ref: Gen.Rel.Gravit.41 (2009) 2301 Abstract: Inflationary cosmology has proved to be the most successful at predicting the properties of the anisotropies observed in the cosmic microwave background (CMB). In this essay we show that quantum field renormalization significantly influences the generation of primordial perturbations and hence the expected measurable imprint of cosmological inflation on the CMB. However, the new predictions remain in agreement with observation, and in fact favor the simplest forms of inflation. In the near future, observations of the influence of gravitational waves from the early universe on the CMB will test our new predictions. |
Title: A Brief Introduction to Loop Quantum Cosmology. Authors: Guillermo A. Mena Marugán. Journal-ref: AIPConf.Proc.1130:89-100 (2009) Abstract: In recent years, Loop Quantum Gravity has emerged as a solid candidate for a nonperturbative quantum theory of General Relativity. It is a background independent theory based on a description of the gravitational field in terms of holonomies and fluxes. In order to discuss its physical implications, a lot of attention has been paid to the application of the quantization techniques of Loop Quantum Gravity to symmetry reduced models with cosmological solutions, a line of research that has been called Loop Quantum Cosmology. We summarize its fundamentals and the main differences with respect to the more conventional quantization approaches employed in cosmology until now. In addition, we comment on the most important results that have been obtained in Loop Quantum Cosmology by analyzing simple homogenous and isotropic models. These results include the resolution of the classical big-bang singularity, which is replaced by a quantum bounce. |
Title: Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC. Authors: Wojciech Kaminski, Jerzy Lewandowski, Tomasz Pawlowski. Journal-ref: Class. Quantum Grav. 26 (2009) 245016 Abstract: A general quantum constraint of the form $C= - \partial_T^2 \otimes B - I\otimes H$ (realized in particular in Loop Quantum Cosmology models) is studied. Group Averaging is applied to define the Hilbert space of solutions and the relational Dirac observables. Two cases are considered. In the first case, the spectrum of the operator $(1/2)\pi^2 B - H$ is assumed to be discrete. The quantum theory defined by the constraint takes the form of a Schroedinger-like quantum mechanics with a generalized Hamiltonian $\sqrt{B^{-1} H}$. In the second case, the spectrum is absolutely continuous and some peculiar asymptotic properties of the eigenfunctions are assumed. The resulting Hilbert space and the dynamics are characterized by a continuous family of the Schroedinger-like quantum theories. However, the relational observables mix different members of the family. Our assumptions are motivated by new Loop Quantum Cosmology models of quantum FRW spacetime. The two cases considered in the paper correspond to the negative and, respectively, positive cosmological constant. Our results should be also applicable in many other general relativistic contexts. |
Title: Hybrid Quantum Cosmology: Combining Loop and Fock Quantizations. Authors: Guillermo A. Mena Marugan, Mercedes Martin-Benito. Journal-ref: Int.J.Mod.Phys.A24:2820-2838,2009 Abstract: As a necessary step towards the extraction of realistic results from Loop Quantum Cosmology, we analyze the physical consequences of including inhomogeneities. We consider in detail the quantization of a gravitational model in vacuo which possesses local degrees of freedom, namely, the linearly polarized Gowdy cosmologies with the spatial topology of a three-torus. We carry out a hybrid quantization which combines loop and Fock techniques. We discuss the main aspects and results of this hybrid quantization, which include the resolution of the cosmological singularity, the polymeric quantization of the internal time, a rigorous definition of the quantum constraints and the construction of their solutions, the Hilbert structure of the physical states, and the recovery of a conventional Fock quantization for the inhomogeneities. |
Title: Dynamical Aspects of Generalized Palatini Theories of Gravity. Authors: Gonzalo J. Olmo, Helios Sanchis-Alepuz, Swapnil Tripathi Journal-ref: Phys. Rev. D 80, 024013 (2009) Abstract: We study the field equations of modified theories of gravity in which the lagrangian is a general function of the Ricci scalar and Ricci-squared terms in Palatini formalism. We show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary metric which, in particular cases of interest, is related with the physical metric by means of a disformal transformation. This relation between physical and auxiliary metric boils down to a conformal transformation in the case of f(R) theories. We also show with explicit models that the inclusion of Ricci squared terms in the action can impose upper bounds on the accessible values of pressure and density, which might have important consequences for the early time cosmology and black hole formation scenarios. Our results indicate that the phenomenology of f(R_{ab}R^{ab}) theories is much richer than that of f(R) and f(R_{ab}R^{ab}) theories and that they also share some similarities with Bekenstein's relativistic theory of MOND. |
Title: Bouncing Cosmologies in Palatini f(R) Gravity Authors: Carlos Barragan, Gonzalo J. Olmo, Helios Sanchis-Alepuz. Journal-ref: Phys.Rev.D 80, 024016, (2009) Abstract: We consider the early time cosmology of f(R) theories in Palatini formalism and study the conditions that guarantee the existence of homogeneous and isotropic models that avoid the Big Bang singularity. We show that for such models the Big Bang singularity can be replaced by a cosmic bounce without violating any energy condition. In fact, the bounce is possible even for pressureless dust. We give a characterization of such models and discuss their dynamics in the region near the bounce. We also find that power-law lagrangians with a finite number of terms may lead to non-singular universes, which contrasts with the infinite-series Palatini f(R) lagrangian that one needs to fully capture the effective dynamics of Loop Quantum Cosmology. We argue that these models could also avoid the formation of singularities during stellar gravitational collapse. |
Title: Insensitivity of Hawking radiation to an invariant Planck-scale cutoff. Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker Journal-ref: Phys.Rev.D80 (2009) 047503. Abstract: A disturbing aspect of Hawking's derivation of black hole radiance is the need to invoke extreme conditions for the quantum field that originates the emitted quanta. It is widely argued that the derivation requires the validity of the conventional relativistic field theory to arbitrarily high, trans-Planckian scales. We stress in this note that this is not necessarily the case if the question is presented in a covariant way. We point out that Hawking radiation is immediately robust against an invariant Planck-scale cutoff. This important feature of Hawking radiation is relevant for a quantum gravity theory that preserves, in some way, the Lorentz symmetry. |
Title:Combinatorics of the SU(2) black hole entropy in loop quantum gravity. Authors: Ivan Agullo, J. Fernando Barbero G., Enrique F. Borja, Jacobo Diaz-Polo, and Eduardo J. S. Villaseñor Journal-ref: Phys.Rev.D80(2009) accepted Abstract: We use the combinatorial and number-theoretical methods developed in previous work by the authors to study black hole entropy in the new proposal put forward by Engle, Noui and Perez. Specifically we give the generating functions relevant for the computation of the entropy and use them to derive its asymptotic behavior including the value of the Immirzi parameter and the coefficient of the logarithmic correction. |
Title: Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I. Authors: Mercedes Martin-Benito, Guillermo A. Mena Marugan, Tomasz Pawlowski. Journal-ref: Phys. Rev. D 80: 084038 (2009) Abstract: We use the vacuum Bianchi I model as an example to investigate the concept of physical evolution in Loop Quantum Cosmology (LQC) in the absence of the massless scalar field which has been used so far in the literature as an internal time. In order to retrieve the system dynamics when no such a suitable clock field is present, we explore different constructions of families of unitarily related partial observables. These observables are parameterized, respectively, by: (i) one of the components of the densitized triad, and (ii) its conjugate momentum; each of them playing the role of an evolution parameter. Exploiting the properties of the considered example, we investigate in detail the domains of applicability of each construction. In both cases the observables possess a neat physical interpretation only in an approximate sense. However, whereas in case (i) such interpretation is reasonably accurate only for a portion of the evolution of the universe, in case (ii) it remains so during all the evolution (at least in the physically interesting cases). The constructed families of observables are next used to describe the evolution of the Bianchi I universe. The performed analysis confirms the robustness of the bounces, also in absence of matter fields, as well as the preservation of the semiclassicality through them. The concept of evolution studied here and the presented construction of observables are applicable to a wide class of models in LQC, including quantizations of the Bianchi I model obtained with other prescriptions for the improved dynamics. |
Title: Flux-area operator and black hole entropy. Authors: J. Fernando Barbero G., Jerzy Lewandowski, and Eduardo J. S. Villaseñor Journal-ref: Phys.Rev.D80(2009)044016 Abstract: We show that, for space-times with inner boundaries, there exists a natural area operator different from the standard one used in loop quantum gravity. This new flux-area operator has equidistant eigenvalues. We discuss the consequences of substituting the standard area operator in the Ashtekar-Baez-Corichi-Krasnov definition of black hole entropy by the new one. Our choice simplifies the definition of the entropy and allows us to consider only those areas that coincide with the one defined by the value of the level of the Chern-Simons theory describing the horizon degrees of freedom. We give a prescription to count the number of relevant horizon states by using spin components and obtain exact expressions for the black hole entropy. Finally we derive its asymptotic behavior, discuss several issues related to the compatibility of our results with the Bekenstein-Hawking area law and the relation with Schwarzschild quasi-normal modes. |
Title: Black hole entropy in loop quantum gravity: The role of internal symmetries. Authors: J. Fernando Barbero G. Journal-ref: J.Phys.:Conf.Ser.175(2009)012005 Abstract: I will discuss here the role of the internal symmetry group in the computations of black hole entropy in loop quantum gravity according to the standard prescription given by Domagala and Lewandowski. In particular I will show how it is possible to take into account the possible choice of either SO(3) or SU(2) as the internal symmetry groups of general relativity in Loop Quantum Gravity and how this choice changes the combinatorial problem of counting the black hole degrees of freedom |
Title: Functional description of S^{1} × S^{2} and S^{3} Gowdy cosmologies. Authors: Daniel Gómez Vergel and Eduardo J. S. Villaseñor Journal-ref: J.Phys.:Conf.Ser.175(2009)012010 Abstract: We will briefly review the classical formulation of the 3-handle S^{1} × S^{2} and 3-sphere S^{3} Gowdy cosmological models coupled with massless scalar fields and their exact (non-perturbative) quantization by defining suitable Schrödinger functional representations in terms of appropriate probability spaces. We will pay special attention to the construction of closed expressions for the corresponding quantum time evolution propagators. |
Title: Semiclassical states for a symmetry reduced gravitational system. Authors: J. Fernando Barbero G., Iñaki Garay, and Eduardo J. S. Villaseñor Journal-ref: AIP Conf.Proc.1122(2009)185-188 Abstract: Einstein-Rosen waves can be exactly quantized. The Hamiltonian operator is a nonlinear, bounded function of the free Hamiltonian corresponding to an axisymmetric massless scalar field propagating in a 2+1 dimensional Minkowskian background. In this short review we will discuss the possibility of constructing true coherent states for this model. We also provide quantitative information about the viability of using the coherent states corresponding to the dynamics of the auxiliary, free Hamiltonian appearing in the description of the system, to study its full physical dynamics. For time periods of arbitrary length we show that this is only possible for states that are close, in a precise mathematical sense, to the vacuum. |
arXives: 0904.3627
Date: 23 April 2009
Subject: gr-qc
Comments: Fourth juried prize in FQXi essay contest on "the Nature of Time"
Title: Condensed matter lessons about the origin of time. Authors: G. Jannes. Abstract: It is widely hoped that quantum gravity will shed a profound light on the origin of time in physics. The currently dominant approaches to a candidate quantum theory of gravity have quite naturally evolved from general relativity, on the one hand, and from particle physics, on the other hand. In this essay, I will argue that a third important branch of 20th century `fundamental' physics, namely condensed-matter physics, also offers an interesting perspective on quantum gravity, and thereby on the problem of time. The bottomline might sound disappointing to those who have become used to claims that quantum gravity or a `Theory of Everything' will solve most of the conceptual problems of fundamental physics: To understand the origin of time, experimental input is needed at much higher energies than what is available today. Moreover, it is far from obvious that we will ever discover the true origin of physical time, even if we become able to directly probe physics at the Planck scale. But we might learn plenty of interesting lessons about time and the structure of our universe in the process. |
Title: Some comments on "The Mathematical Universe" Authors: G. Jannes. Journal-ref: Found. Phys. 39: 397-406 (2009) Abstract: I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of which lies in the acceptance that mathematics is (at least in part) a human construction, and discuss concrete consequences of this--at first sight purely philosophical--difference in point of view. |
Title: Uniqueness of the Fock quantization of a free scalar field on $S^1$ with time dependent mass. Authors: Jerónimo Cortez, Guillermo A. Mena Marugán, Rogério Serôdio, José M. Velhinho. Journal-ref: Phys. Rev. D79:084040 (2009) Abstract: We analyze the quantum description of a free scalar field on the circle in the presence of an explicitly time dependent potential, also interpretable as a time dependent mass. Classically, the field satisfies a linear wave equation of the form $\ddot{\xi}-\xi"+f(t)\xi=0$. We prove that the representation of the canonical commutation relations corresponding to the particular case of a massless free field ($f=0$) provides a unitary implementation of the dynamics for sufficiently general mass terms, $f(t)$. Furthermore, this representation is uniquely specified, among the class of representations determined by $S^1$-invariant complex structures, as the only one allowing a unitary dynamics. These conclusions can be extended in fact to fields on the two-sphere possessing axial symmetry. This generalizes a uniqueness result previously obtained in the context of the quantum field description of the Gowdy cosmologies, in the case of linear polarization and for any of the possible topologies of the spatial sections. |
Title: A complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole. Authors: David Brizuela, Jose M. Martin-Garcia, Manuel Tiglio. Journal-ref: Phys.Rev.D80:024021 (2009) Abstract: Using recently developed efficient symbolic manipulations tools, we present a general gauge-invariant formalism to study arbitrary radiative $(l\geq 2)$ second-order perturbations of a Schwarzschild black hole. In particular, we construct the second order Zerilli and Regge-Wheeler equations under the presence of any two first-order modes, reconstruct the perturbed metric in terms of the master scalars, and compute the radiated energy at null infinity. The results of this paper enable systematic studies of generic second order perturbations of the Schwarzschild spacetime. In particular, studies of mode-mode coupling and non-linear effects in gravitational radiation, the second-order stability of the Schwarzschild spacetime, or the geometry of the black hole horizon. |
Title: The time-dependent quantum harmonic oscillator revisited: applications to quantum field theory. Authors: Daniel Gómez Vergel and Eduardo J. S. Villaseñor Journal-ref: Ann.Phys.324(2009)1360-1385 Abstract: In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a single one-dimensional time-dependent oscillator, for which we first summarize some basic results concerning the unitary implementability of the dynamics. This is done by employing techniques different from those used so far to derive the Feynman propagator. In particular, we calculate the transition amplitudes for the usual harmonic oscillator eigenstates and define suitable semiclassical states for some physically relevant models. We then explore the possible extension of this study to infinite dimensional dynamical systems. Specifically, we construct Schroedinger functional representations in terms of appropriate probability spaces, analyze the unitarity of the time evolution, and probe the existence of semiclassical states for a wide range of physical systems, particularly, the well-known Minkowskian free scalar fields and Gowdy cosmological models. |
Title: Big Bounce and inhomogeneities. Authors: David Brizuela, Guillermo A. Mena Marugan, Tomasz Pawlowski Journal-ref: Class.Quant.Grav.27: 052001 (2010) Abstract: The dynamics of an inhomogeneous universe is studied with the methods of Loop Quantum Cosmology as an example of the quantization of vacuum cosmological spacetimes containing gravitational waves (Gowdy spacetimes). The analysis performed at the effective level shows that: (i) The initial Big Bang singularity is replaced (as in the case of homogeneous cosmological models) by a Big Bounce, joining deterministically two large universes, (ii) the universe size at the bounce is at least of the same order of magnitude as that of the background homogeneous universe, (iii) for each gravitational wave mode, the difference in amplitude at very early and very late times has a vanishing statistical average when the bounce dynamics is strongly dominated by the inhomogeneities, whereas this average is positive when the dynamics is in a near-vacuum regime, so that statistically the inhomogeneities are amplified. |
Title: Revising the predictions of inflation for the cosmic microwave background anisotropies. Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker Journal-ref: Phys. Rev. Lett. 103, 061301 (2009) Abstract: Inflationary cosmology predicts that, due to quantum effects, small density perturbations are generated in the very early universe with a nearly "scale-free" spectrum. The detection and analysis of anisotropies in the cosmic microwave background has spectacularly confirmed this prediction. Moreover, inflation also predicts the creation of primordial gravitational waves, which still remain undetectable. Forthcoming high-precision measurements of the cosmic microwave background may measure effects of relic gravitational waves, and this will be crucial to test the inflationary paradigm and strongly constrain inflationary models. Therefore, it is particularly important to scrutinize, from all points of view, the quantitative predictions of inflation. In this work we point out that if quantum field renormalization is taken into account, the predictions of slow- roll inflation for both the scalar and tensorial power spectrum change significantly. This leads, in particular, to a change in the consistency condition that relates the tensor-to-scalar amplitude ratio r with spectral indices. Moreover, a reexamination of the chaotic potentials \phi^2, \phi^4, shows that both fall well inside the 68% confidence level region in the plane (n_s, r) of the five-year WMAP data. In contrast, the standard predictions rule out the potential \phi^4. The alternative predictions presented in this work may soon come within the range of measurement of near-future experiments. |
Title: On the computation of black hole entropy in loop quantum gravity. Authors: J. Fernando Barbero G. and Eduardo J. S. Villaseñor Journal-ref: Class.Quant.Grav.26(2009)035017 Abstract: We discuss some issues related to the computation of black hole entropy in loop quantum gravity from the novel point of view provided by the recent number-theoretical methods introduced by the authors and their collaborators. In particular we give exact expressions, in the form of integral transforms, for the black hole entropy in terms of the area. We do this by following several approaches based both on our combinatorial techniques and also on functional equations similar to those employed by Meissner in his pioneering work on this subject. To put our results in perspective we compare them with those of Meissner. We will show how our methods confirm some of his findings, extend the validity of others, and correct some mistakes. At the end of the paper we will discuss the delicate issue of the asymptotics of black hole entropy. |
Title: On the condensed matter scheme for emergent gravity and interferometry. Authors: G. Jannes. Journal-ref: "Interferometers: Research, Technology and Applications" Abstract: An increasingly popular approach to quantum gravity rests on the idea that gravity (and maybe electromagnetism and the other gauge fields) might be an 'emergent phenomenon', in the sense of representing a collective behaviour resulting from a very different microscopic physics. A prominent example of this approach is the condensed matter scheme for quantum gravity, which considers the possibility that gravity emerges as an effective low-energy phenomenon from the quantum vacuum in a way similar to the emergence of collective excitations in condensed matter systems. This condensed matter view of the quantum vacuum clearly hints that, while the term 'ether' has been discredited for about a century, quantum gravity holds many (if not all) of the characteristics that have led people in the past to label various hypothetical substances with the term 'ether'. Since the last burst of enthusiasm for an ether, at the end of the 19th century, was brought to the grave in part by the performance of a series of important experiments in interferometry, the suggestion then naturally arises that maybe interferometry could also play a role in the current discussion on quantum gravity. We will highlight some aspects of this suggestion in the context of the condensed matter scheme for emergent gravity. |
Title: Physical time and other conceptual issues of QG on the example of LQC Authors: Wojciech Kaminski, Jerzy Lewandowski, Tomasz Pawlowski. Journal-ref: Class. Quantum Grav. 26 (2009) 035012 Abstract: Several conceptual aspects of quantum gravity are studied on the example of the homogeneous isotropic LQC model. In particular: (i) The relativistic time of the co-moving observers is showed to be a quantum operator and a quantum spacetime metric tensor operator is derived. (ii) Solutions of the quantum scalar constraint for two different choices of the lapse function are compared and contrasted. (iii) The mechanism of the singularity avoidance is analyzed via detailed studies of an energy density operator. (iv) The relation between the kinematical and the physical quantum geometry is discussed on the level of relation between observables. |
Title: Sensitivity of Hawking radiation to superluminal dispersion relations. Authors: C. Barcelo, L.J. Garay, G. Jannes. Journal-ref: Phys. Rev. D 79: 024016 (2009) Abstract: We analyze the Hawking radiation process due to collapsing configurations in the presence of superluminal modifications of the dispersion relation. With such superluminal dispersion relations, the horizon effectively becomes a frequency-dependent concept. In particular, at every moment of the collapse, there is a critical frequency above which no horizon is experienced. We show that, as a consequence, the late-time radiation suffers strong modifications, both quantitative and qualitative, compared to the standard Hawking picture. Concretely, we show that the radiation spectrum becomes dependent on the measuring time, on the surface gravities associated with different frequencies, and on the critical frequency. Even if the critical frequency is well above the Planck scale, important modifications still show up. |
Title: xPert: Computer algebra for metric perturbation theory. Authors: David Brizuela, José M. Martín-García, Guillermo A. Mena Marugán. Journal-ref: Gen. Rel. Grav. 41: 2415-2431 (2009) Abstract: We present the tensor computer algebra package xPert for fast construction and manipulation of the equations of metric perturbation theory, around arbitrary backgrounds. It is based on the combination of explicit combinatorial formulas for the n-th order perturbation of curvature tensors and their gauge changes, and the use of highly efficient techniques of index canonicalization, provided by the underlying tensor system xAct, for Mathematica. We give examples of use and show the efficiency of the system with timings plots: it is possible to handle orders n=4 or n=5 within seconds, or reach n=10 with timings below 1 hour. |
Title: Effective Action for Loop Quantum Cosmology a la Palatini Authors: Gonzalo J. Olmo, Parampreet Singh Journal-ref: JCAP 01 (2009) 030 Abstract: The resolution of the big bang singularity in loop quantum cosmology can be described by quantum gravitational modifications to the Friedman dynamics without introducing any new degrees of freedom. A challenging question is to construct a covariant effective action able to reproduce that new physics emergent at the Planck scale. By enlarging our scope to the realm of non-metric theories, we show that apparent tensions with conventional approaches can be overcome. We provide an algorithm to construct an effective action for loop quantum cosmology in the Palatini framework and obtain an action which involves an infinite series in the scalar curvature of the independent connection. This effective action successfully captures non-local quantum geometric effects and the non-singular bounce at the Planck scale and leads to general relativity at low curvatures. |
Title: Hamiltonian theory for the axial perturbations of a dynamical spherical background Authors: David Brizuela, Jose M. Martin-Garcia Journal-ref: Class.Quant.Grav.26,015003 (2009) Abstract: We develop the Hamiltonian theory of axial perturbations around a general time-dependent spherical background spacetime. Using the fact that the linearized constraints are gauge generators, we isolate the physical and unconstrained axial gravitational wave in a Hamiltonian pair of variables. Then, switching to a more geometrical description of the system, we construct the only scalar combination of them. We obtain the well-known Gerlach and Sengupta scalar for axial perturbations, with no known equivalent for polar perturbations. The strategy suggested and tested here will be applied to the polar case in a separate article. |
Title: Re-examination of Polytropic Spheres in Palatini f(R) Gravity. Authors: Gonzalo J. Olmo Journal-ref: Phys.Rev.D 78, 104026 (2008) Abstract: We investigate spherically symmetric, static matter configurations with polytropic equation of state for a class of f(R) models in Palatini formalism and show that the surface singularities recently reported in the literature are not physical in the case of Planck scale modified lagrangians. In such cases, they are just an artifact of the idealized equation of state used. In fact, we show that for the models f(R)=R\pm\lambda R^2, with \lambda on the order of the Planck length squared, the presence of a single electron in the Universe would be enough to cure all stellar singularities of this type. From our analysis it also follows that the stellar structure derived from these lagrangians is virtually undistinguishable from that corresponding to General Relativity. For ultraviolet corrected models far from the Planck scale, however, the surface singularities may indeed arise in the region of validity of the polytropic equation of state. This fact can be used to place constraints on the parameters of particular models. |
Title: Quantum Einstein-Rosen waves: Coherent states and n-point functions Authors: J. Fernando Barbero G., Iñaki Garay, and Eduardo J. S. Villaseñor Journal-ref: Class.Quant.Grav.25,205013 (2008). Abstract: We discuss two different types of issues concerning the quantization of Einstein-Rosen waves. First of all we study in detail the possibility of using the coherent states corresponding to the dynamics of the auxiliary, free Hamiltonian appearing in the description of the model to study the full dynamics of the system. For time periods of arbitrary length we show that this is only possible for states that are close, in a precise mathematical sense, to the vacuum. We do this by comparing the quantum evolutions defined by the auxiliary and physical Hamiltonians on the class of coherent states. In the second part of the paper we study the structure of n-point functions. As we will show their detailed behavior differs from the one corresponding to standard perturbative quantum field theories. We take this as a manifestation of the fact that the correct approximation scheme for physically interesting objects in these models does not lead to a power series expansion in the relevant coupling constant but to a more complicated asymptotic behavior. |
arXives: 0806.0034
Date: 30 May 2008
Subject: QFT
Comments: Letter. See a comment of this paper in Physics.
Title: Generating functions for black hole entropy in loop quantum gravity Authors: J. Fernando Barbero G. and Eduardo J. S. Villaseñor Journal-ref: Phys.Rev.D77, 121502(R) (2008) Abstract: We introduce, in a systematic way, a set of generating functions that solve all the different combinatorial problems that crop up in the study of black hole entropy in loop quantum gravity. Specifically we give generating functions for the following: the different sources of degeneracy related to the spectrum of the area operator, the solutions to the projection constraint, and the black hole degeneracy spectrum. Our methods are capable of handling the different countings proposed and discussed in the literature. The generating functions presented here provide the appropriate starting point to extend the results already obtained for microscopic black holes to the macroscopic regimein particular those concerning the area law and the appearance of an effectively equidistant area spectrum. |
Title: Loop Quantization of Vacuum Bianchi I Cosmology. Authors: M. Martín-Benito, G.A. Mena Marugán, T. Pawlowski. Journal-ref: Phys. Rev. D 78, 064008 (2008) Abstract: We analyze the loop quantization of the family of vacuum Bianchi I spacetimes, a gravitational system whose classical solutions describe homogeneous anisotropic cosmologies. We rigorously construct the operator that represents the Hamiltonian constraint, showing that the states of zero volume completely decouple from the rest of quantum states. This fact ensures that the classical cosmological singularity is resolved in the quantum theory. In addition, this allows us to adopt an equivalent quantum description in terms of a well defined densitized Hamiltonian constraint. This latter constraint can be regarded in a certain sense as a difference evolution equation in an internal time provided by one of the triad components, which is polymerically quantized. Generically, this evolution equation is a relation between the projection of the quantum states in three different sections of constant internal time. Nevertheless, around the initial singularity the equation involves only the two closest sections with the same orientation of the triad. This has a double effect: on the one hand, physical states are determined just by the data on one section, on the other hand, the evolution defined in this way never crosses the singularity, without the need of any special boundary condition. Finally, we provide these physical states with a Hilbert structure, completing the quantization. |
Title: Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations. Authors: Mercedes Martín-Benito, Luis J. Garay, Guillermo A. Mena Marugán. Journal-ref: Phys.Rev.D 78, 083516 (2008) Abstract: We quantize an inhomogeneous cosmological model using techniques that include polymeric quantization. More explicitly, we construct well defined operators to represent the constraints and find the physical Hilbert space formed by their solutions, which reproduces the conventional Fock quantization for the inhomogeneities. The initial singularity is resolved in this inhomogeneous model in an extremely simple way and without imposing special boundary conditions, thus ensuring the robustness and generality of this resolution. Furthermore this quantization constitutes a well founded step towards the extraction of physical results and consequences from loop quantum cosmology, given the central role of the inhomogeneities in modern cosmology. |
Title: Introduction to Quantum Mechanics Authors: Eduardo J. S. Villaseñor Journal-ref: AIP Conf.Proc.1023, 107-117 (2008) Abstract: The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed. |
Title: Quantum Geometry and Quantum Gravity Authors: J. Fernando Barbero G. Journal-ref: AIP Conf.Proc.1023, 3-33 (2008) Abstract: The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues concerning the relationship of the formalism with other more traditional approaches inspired in the treatment of the fundamental interactions in the standard model. Mathematically I will pay special attention to functional analytic issues, the construction of the relevant Hilbert spaces and the definition and properties of geometric operators: areas and volumes. |
Title: Anti-deSitter universe dynamics in LQC Authors: Eloisa Bentivegna, Tomasz Pawlowski. Journal-ref: http://dx.doi.org/10.1103/PhysRevD.77.124025">Phys.Rev.D77:124025 (2008) Abstract: A model for a flat isotropic universe with a negative cosmological constant $\Lambda$ and a massless scalar field as sole matter content is studied within the framework of Loop Quantum Cosmology. By application of the methods introduced for the model with $\Lambda=0$, the physical Hilbert space and the set of Dirac observables are constructed. As in that case, the scalar field plays here the role of an emergent time. The properties of the system are found to be similar to those of the $k=1$ FRW model: for small energy densities, the quantum dynamics reproduces the classical one, whereas, due to modifications at near-Planckian densities, the big bang and big crunch singularities are replaced by a quantum bounce connecting deterministically the large semiclassical epochs. Thus in Loop Quantum Cosmology the evolution is qualitatively cyclic. |
Title: Black hole state counting in loop quantum gravity: A number-theoretical approach Authors: Ivan Agullo, J. Fernando Barbero G., Jacobo Diaz-Polo, Enrique Fernandez-Borja, and Eduardo J. S. Villaseñor Journal-ref: Phys.Rev.Lett.100, 211301 (2008) Abstract: We give an efficient method, combining number-theoretic and combinatorial ideas, to exactly compute black hole entropy in the framework of loop quantum gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and explicitly determine the number of solutions to the projection constraint. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum. |
Title: Schrodinger quantization of linearly polarized Gowdy S^{1} × S^{2} and S^{3} models coupled to massless scalar fields Authors: Daniel Gómez Vergel Journal-ref: Class.Quant.Grav.25, 175016 (2008) Abstract: In this paper, we will construct the Schrödinger representation for the linearly polarized Gowdy S^{1} × S^{2} and S^{3} models coupled to massless scalar fields. Here the quantum states belong to a L^{2}-space for a suitable quantum configuration space endowed with a Gaussian measure, whose support is analyzed. This study completes the quantization of these systems previously performed in the Fock scheme, and provides a specially useful framework to address physically relevant questions. |
Title: Unitary evolution of free massless fields in de Sitter space-time Authors: Daniel Gómez Vergel and Eduardo J. S. Villaseñor Journal-ref: Class.Quant.Grav. 25, 145008 (2008) Abstract: We consider the quantum dynamics of a massless scalar field in de Sitter space-time. The classical evolution is represented by a canonical transformation on the phase space for the field theory. By studying the corresponding Bogoliubov transformations, we show that the symplectic map that encodes the evolution between two instants of time cannot be unitarily implemented on any Fock space built from a SO(4)-symmetric complex structure. We will show also that, in contrast with some effectively lower dimensional examples arising from Quantum General Relativity such as Gowdy models, it is impossible to find a time dependent conformal redefinition of the massless scalar field leading to a quantum unitary dynamics. |
Title: Quantum unitary evolution of linearly polarized S^{1} × S^{2} and S^{3} Gowdy models coupled to massless scalar fields Authors: J. Fernando Barbero G., Daniel Gómez Vergel, and Eduardo J. S. Villaseñor Journal-ref: Class.Quant.Grav.25, 085002 (2008) Abstract: The purpose of this paper is to study in detail the problem of defining unitary evolution for linearly polarized S^{1} × S^{2} and S^{3} Gowdy models (in vacuum or coupled to massless scalar fields). We show that in the Fock quantizations of these systems no choice of acceptable complex structure leads to a unitary evolution for the original variables. Nonetheless, unitarity can be recovered by suitable redefinitions of the basic fields. These are dictated by the time dependent conformal factors that appear in the description of the standard deparameterized form of these models as field theories in certain curved backgrounds. We also show the unitary equivalence of the Fock quantizations obtained from the SO(3)-symmetric complex structures for which the dynamics is unitarily implemented. |
Title: Uniqueness of the Fock representation of the Gowdy S^{1} × S^{2} and S^{3} models. Authors: Jerónimo Cortez, Guillermo A. Mena Marugán, José M. Velhinho Journal-ref: Class. Quant. Grav.25, 105005 (2008) Abstract: After a suitable gauge fixing, the local gravitational degrees of freedom of the Gowdy S^{1} × S^{2} and S^{3} cosmologies are encoded in an axisymmetric field on the sphere S^{2}. Recently, it has been shown that a standard field parametrization of these reduced models admits no Fock quantization with a unitary dynamics. This lack of unitarity is surpassed by a convenient redefinition of the field and the choice of an adequate complex structure. The result is a Fock quantization where both the dynamics and the SO(3)-symmetries of the field equations are unitarily implemented. The present work proves that this Fock representation is in fact unique inasmuch as, up to equivalence, there exists no other possible choice of SO(3)-invariant complex structure leading to a unitary implementation of the time evolution. |
Title: Classical and quantum behavior of dynamical systems defined by functions of solvable Hamiltonians Authors: J. Fernando Barbero G., Iñaki Garay, and Eduardo J. S. Villaseñor Journal-ref: Am.J.Phys. 76, 153-157 (2008) Abstract: We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the harmonic oscillator is emphasized. We show that, in spite of the similarities at the classical level, the quantum evolution is very different. In particular, this difference is important in constructing coherent states, which is impossible in most cases. The class of Hamiltonians we consider is interesting due to its pedagogical value and its applicability to some open research problems in quantum optics and quantum gravity. |
Title: Hamiltonian dynamics of linearly polarized Gowdy models coupled to massless scalar fields Authors: J. Fernando Barbero G., Daniel Gómez Vergel, and Eduardo J. S. Villaseñor Journal-ref: Class.Quant.Grav.24 (2007) 5945-5972 Abstract: The purpose of this paper is to analyze in detail the Hamiltonian formulation for the compact Gowdy models coupled to massless scalar fields as a necessary first step towards their quantization. We will pay special attention to the coupling of matter and those features that arise for the three-handle and three-sphere topologies that are not present in the well studied three torus case -in particular the polar constraints that come from the regularity conditions on the metric. As a byproduct of our analysis we will get an alternative understanding, within the Hamiltonian framework, of the appearance of initial and final singularities for these models. |
Title: Quantum Gowdy T3 model: Schrodinger representation with unitary dynamics. Authors: Alejandro Corichi, Jerónimo Cortez, Guillermo A. Mena Marugán, José M. Velhinho. Journal-ref: Phys. Rev. D 76, 124031 (2007) Abstract: The linearly polarized Gowdy $T^3$ model is paradigmatic for studying technical and conceptual issues in the quest for a quantum theory of gravity since, after a suitable and almost complete gauge fixing, it becomes an exactly soluble midisuperspace model. Recently, a new quantization of the model, possessing desired features such as a unitary implementation of the gauge group and of the time evolution, has been put forward and proven to be essentially unique. An appropriate setting for making contact with other approaches to canonical quantum gravity is provided by the Schr\"odinger representation, where states are functionals on the configuration space of the theory. Here we construct this functional description, analyze the time evolution in this context and show that it is also unitary when restricted to physical states, i.e. states which are solutions to the remaining constraint of the theory. |
Title: Quantum time uncertainty in Schwarzschild-anti-de Sitter black holes. Authors: Pablo Galán, Luis J. Garay, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 76, 044014 (2007) Abstract: The combined action of gravity and quantum mechanics gives rise to a minimum time uncertainty in the lowest order approximation of a perturbative scheme, in which quantum effects are regarded as corrections to the classical spacetime geometry. From the nonperturbative point of view, both gravity and quantum mechanics are treated on equal footing in a description that already contains all possible backreaction effects as those above in a nonlinear manner. In this paper, the existence or not of such minimum time uncertainty is analyzed in the context of Schwarzschild-anti-de Sitter black holes using the isolated horizon formalism. We show that from a perturbative point of view, a nonzero time uncertainty is generically present owing to the energy scale introduced by the cosmological constant, while in a quantization scheme that includes nonperturbatively the effects of that scale, an arbitrarily high time resolution can be reached. |
Title: High-order gauge-invariant perturbations of a spherical spacetime. Authors: David Brizuela, José M. Martín-García, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 76, 024004 (2007) Abstract: We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general algorithm to construct these invariants and provide explicit formulas for the case of second-order metric perturbations. We show that the well-known problem of lack of invariance for the first-order perturbations with l=0,1 propagates to increasing values of l for perturbations of higher order, owing to mode coupling. We also discuss in which circumstances it is possible to construct the invariants. |
Title: Uniqueness of the Fock quantization of the Gowdy T3 model. Authors: Jerónimo Cortez, Guillermo A. Mena Marugán, José M. Velhinho. Journal-ref: Phys. Rev. D 75, 084027 (2007) Abstract: After its reduction by a gauge-fixing procedure, the family of linearly polarized Gowdy $T^3$ cosmologies admit a scalar field description whose evolution is governed by a Klein-Gordon type equation in a flat background in 1+1 dimensions with the spatial topology of $S^1$, though in the presence of a time-dependent potential. The model is still subject to a homogeneous constraint, which generates $S^1$-translations. Recently, a Fock quantization of this scalar field was introduced and shown to be unique under the requirements of unitarity of the dynamics and invariance under the gauge group of $S^1$-translations. In this work, we extend and complete this uniqueness result by considering other possible scalar field descriptions, resulting from reasonable field reparameterizations of the induced metric of the reduced model. In the reduced phase space, these alternate descriptions can be obtained by means of a time-dependent scaling of the field, the inverse scaling of its canonical momentum, and the possible addition of a time-dependent, linear contribution of the field to this momentum. Demanding again unitarity of the field dynamics and invariance under the gauge group, we prove that the alternate canonical pairs of fieldlike variables admit a Fock representation if and only if the scaling of the field is constant in time. In this case, there exists essentially a unique Fock representation, provided by the quantization constructed by Corichi, Cortez, and Mena Marugan. In particular, our analysis shows that the scalar field description proposed by Pierri does not admit a Fock quantization with the above unitarity and invariance properties. |
Title: Canonical Realizations of Doubly Special Relativity. Authors: Pablo Galán, Guillermo A. Mena Marugán. Journal-ref: Int. J. Mod. Phys. D 16, 1133 (2007) Abstract: The linear relation between the entropy and area of a black hole can be derived from the Heisenberg principle, the energy-momentum dispersion relation of special relativity, and general considerations about black holes. There exist results in quantum gravity and related contexts suggesting the modification of the usual dispersion relation and uncertainty principle. One of these contexts is the gravity's rainbow formalism. We analyze the consequences of such a modification for black hole thermodynamics from the perspective of two distinct rainbow realizations built from doubly special relativity. One is the proposal of Magueijo and Smolin and the other is based on a canonical implementation of doubly special relativity put forward recently by the authors. In these scenarios, we obtain modified expressions for the entropy and temperature of black holes. We show that, for a family of doubly special relativity theories satisfying certain properties, the temperature can vanish in the limit of zero black hole mass. For the Magueijo and Smolin proposal, this is only possible for some restricted class of models with bounded energy and unbounded momentum. With the proposal of a canonical implementation, on the other hand, the temperature may vanish for more general theories; in particular, the momentum may also be bounded, with bounded or unbounded energy. This opens new possibilities for the outcome of black hole evaporation in the framework of a gravity's rainbow. |
arXives:gr-qc/0701173
Date: 31 Jan 2007
Subject: Analogue gravity, condensed matter
Comments: Reg.article
Title: Quasi-normal mode analysis in BEC acoustic black holes Authors: C. Barcelo, A. Cano, L.J. Garay, G. Jannes Journal-ref: Phys.Rev.D75:084024 (2007) Abstract: We perform a quasi-normal mode analysis of black hole configurations in Bose-Einstein condensates (BEC). In this analysis we use the full Bogoliubov dispersion relation, not just the hydrodynamic or geometric approximation. We restrict our attention to one-dimensional flows in BEC with step-like discontinuities. For this case we show that in the hydrodynamic approximation quasi-normal modes do not exist. The full dispersion relation, however, allows the existence of quasi-normal modes. Remarkably, the spectrum of these modes is not discrete but continuous. |
Title: Thermodynamics of Black Holes in Gravity's Rainbow Formalisms. Authors: Pablo Galán, Guillermo A. Mena Marugán. Journal-ref: J. Phys. Conf. Ser. 66, 12036 (2007) Abstract: Several results in the context of quantum gravity and related frameworks suggest the plausibility of modifications to the uncertainty principle and to the energy-momentum dispersion relation of special relativity. One of these frameworks is provided by gravity's rainbow. We analyze the consequences that such modifications may have for black hole thermodynamics from the perspective of two different gravity's rainbow formalisms. In this scenario, we show that the temperature of the black hole may vanish in the limit of zero mass under feasible conditions. |
arXives: no entry
Date: December 2006
Subject: Numerical Relativity
Comments: Conference proceedings
Title: High-order gauge-invariant perturbations of a spherical spacetime. Authors: David Brizuela, José M. Martín-García, Guillermo A. Mena Marugán. Journal-ref: J. Phys. Conf. Ser. 66, 012011 (2007) Abstract: We construct a covariant and gauge-invariant framework to deal with arbitrary high-order perturbations of a spherical spacetime. It can be regarded as the generalization to high orders of the Gerlach and Sengupta formalism for first-order nonspherical perturbations. The Regge-Wheeler-Zerilli harmonics are generalized to an arbitrary number of indices and a closed formula is deduced for their products. An iterative procedure is given in order to construct gauge-invariant quantities up to any perturbative order. Focusing on second-order perturbation theory, we explicitly compute the sources for the gauge invariants as well as for the evolution equations. |
Title: Entropy and temperature of black holes in a gravity's rainbow. Authors: Pablo Galán, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 74, 044035 (2006) Abstract: The linear relation between the entropy and area of a black hole can be derived from the Heisenberg principle, the energy-momentum dispersion relation of special relativity, and general considerations about black holes. There exist results in quantum gravity and related contexts suggesting the modification of the usual dispersion relation and uncertainty principle. One of these contexts is the gravity's rainbow formalism. We analyze the consequences of such a modification for black hole thermodynamics from the perspective of two distinct rainbow realizations built from doubly special relativity. One is the proposal of Magueijo and Smolin and the other is based on a canonical implementation of doubly special relativity put forward recently by the authors. In these scenarios, we obtain modified expressions for the entropy and temperature of black holes. We show that, for a family of doubly special relativity theories satisfying certain properties, the temperature can vanish in the limit of zero black hole mass. For the Magueijo and Smolin proposal, this is only possible for some restricted class of models with bounded energy and unbounded momentum. With the proposal of a canonical implementation, on the other hand, the temperature may vanish for more general theories; in particular, the momentum may also be bounded, with bounded or unbounded energy. This opens new possibilities for the outcome of black hole evaporation in the framework of a gravity's rainbow. |
Title: Probing quantized Einstein-Rosen waves with massless scalar matter Authors: J. Fernando Barbero G., Iñaki Garay, and Eduardo J. S. Villaseñor Journal-ref: Phys.Rev.D74 (2006) 044004 Abstract: The purpose of this paper is to discuss in detail the use of scalar matter coupled to linearly polarized Einstein-Rosen waves as a probe to study quantum gravity in the restricted setting provided by this symmetry reduction of general relativity. We will obtain the relevant Hamiltonian and quantize it with the techniques already used for the purely gravitational case. Finally we will discuss the use of particle-like modes of the quantized fields to operationally explore some of the features of quantum gravity within this framework. Specifically we will study two-point functions, the Newton-Wigner propagator, and radial wave functions for one-particle states. |
Title: Quantum Gowdy T3 model: A Uniqueness result. Authors: Alejandro Corichi, Jerónimo Cortez, Guillermo A. Mena Marugán, José M. Velhinho Journal-ref: Class. Quant. Grav. 23, 6301 (2006) Abstract: Modulo a homogeneous degree of freedom and a global constraint, the linearly polarised Gowdy $T^3$ cosmologies are equivalent to a free scalar field propagating in a fixed nonstationary background. Recently, a new field parameterisation was proposed for the metric of the Gowdy spacetimes such that the associated scalar field evolves in a flat background in 1+1 dimensions with the spatial topology of $S^1$, although subject to a time dependent potential. Introducing a suitable Fock quantisation for this scalar field, a quantum theory was constructed for the Gowdy model in which the dynamics is implemented as a unitary transformation. A question that was left open is whether one might adopt a different, nonequivalent Fock representation by selecting a distinct complex structure. The present work proves that the chosen Fock quantisation is in fact unique (up to unitary equivalence) if one demands unitary implementation of the dynamics and invariance under the group of constant $S^1$ translations. These translations are precisely those generated by the global constraint that remains on the Gowdy model. It is also shown that the proof of uniqueness in the choice of complex structure can be applied to more general field dynamics than that corresponding to the Gowdy cosmologies. |
Title: Second and higher-order perturbations of a spherical spacetime. Authors: David Brizuela, José M. Martín-García, Guillermo A. Mena Marugán. Journal-ref: Phys.Rev.D74, 044039 (2006) Abstract: The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory. The GS harmonics are generalized to an arbitrary number of indices on the unit sphere and a formula is given for their products. The formalism is optimized for its implementation in a computer algebra system, something that becomes essential in practice given the size and complexity of the equations. All evolution equations for the second-order perturbations, as well as the conservation equations for the energy-momentum tensor at this perturbation order, are given in covariant form, in Regge-Wheeler gauge. |
Title: Evolution operators for linearly polarized two-Killing cosmological models Authors: J. Fernando Barbero G., Daniel Gómez Vergel, and Eduardo J. S. Villaseñor Journal-ref: Phys.Rev.D74 (2006) 024003 Abstract: We give a general procedure to obtain non perturbative evolution operators in closed form for quantized linearly polarized two Killing vector reductions of general relativity with a cosmological interpretation. We study the representation of these operators in Fock spaces and discuss in detail the conditions leading to unitary evolutions. |
Title: Quantum Gowdy T3 model: A Unitary description. Authors: Alejandro Corichi, Jerónimo Cortez, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 73, 084020 (2006) Abstract: The quantization of the family of linearly polarized Gowdy T3 spacetimes is discussed in detail, starting with a canonical analysis in which the true degrees of freedom are described by a scalar field that satisfies a Klein-Gordon type equation in a fiducial time-dependent background. A time-dependent canonical transformation, which amounts to a change of the basic (scalar) field of the model, brings the system to a description in terms of a Klein-Gordon equation on a background that is now static, although subject to a time-dependent potential. The system is quantized by means of a natural choice of annihilation and creation operators. The quantum time evolution is considered and shown to be unitary, so that both the Schrödinger and Heisenberg pictures can be consistently constructed. This has to be contrasted with previous treatments for which time evolution failed to be implementable as a unitary transformation. Possible implications for both canonical quantum gravity and quantum field theory in curved spacetime are noted. |
arXives:gr-qc/0603089
Date: 22 Mar 2006
Subject: Analogue gravity, condensed matter
Comments: Reg.article
Title: Stability analysis of sonic horizons in Bose-Einstein condensates Authors: C. Barcelo, A. Cano, L.J. Garay, G. Jannes Journal-ref: Phys.Rev.D74:024008 (2006) Abstract: We examine the linear stability of various configurations in Bose-Einstein condensates with sonic horizons. These configurations are chosen in analogy with gravitational systems with a black hole horizon, a white hole horizon and a combination of both. We discuss the role of different boundary conditions in this stability analysis, paying special attention to their meaning in gravitational terms. We highlight that the stability of a given configuration, not only depends on its specific geometry, but especially on these boundary conditions. Under boundary conditions directly extrapolated from those in standard General Relativity, black hole configurations, white hole configurations and the combination of both into a black hole--white hole configuration are shown to be stable. However, we show that under other (less stringent) boundary conditions, configurations with a single black hole horizon remain stable, whereas white hole and black hole--white hole configurations develop instabilities associated to the presence of the sonic horizons. |
Title: Unitary evolution in Gowdy cosmology. Authors: Alejandro Corichi, Jerónimo Cortez, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 73, 041502 (2006) Abstract: Recent results on the nonunitary character of quantum time evolution in the family of Gowdy T3 spacetimes bring the question of whether one should abandon the most sacred principle of unitary evolution in cosmology. In this work we show that the answer is in the negative. We put forward a full nonperturbative canonical quantization of the polarized Gowdy T3 model that implements the dynamics while preserving unitarity. We discuss possible implications of this result. |
Title: Unitary time evolution in the Gowdy T3 model. Authors: Jerónimo Cortez, Guillermo A. Mena Marugán Journal-ref: J. Phys. Conf. Ser. 33, 330 (2006) Abstract: The polarized Gowdy T3 model is a classically solvable cosmological model with local degrees of freedom. This explains the increasing interest in its quantization. After gauge fixing, the system can be described in terms of a point particle and a massless scalar field propagating in an expanding torus. A Fock space representation has been proposed for the quantization of the model, but the classical dynamics for the scalar field cannot be unitarily implemented in this quantum theory. We show that, nevertheless, unitarity can be regained by slightly modifying the dynamics with quantum corrections. Moreover, a time-dependent rescaling of the scalar field leads to new evolution equations that can be unitarily implemented. |
Title: Feasibility of a unitary quantum dynamics in the Gowdy T3 cosmological model. Authors: Jerónimo Cortez, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 72, 064020 (2005) Abstract: It has been pointed out that it is impossible to obtain a unitary implementation of the dynamics for the polarized Gowdy T3 cosmologies in an otherwise satisfactory, nonperturbative canonical quantization proposed for these spacetimes. By introducing suitable techniques to deal with deparametrized models in cosmology that possess an explicit time dependence (as it is the case for the toroidal Gowdy model), we present in this paper a detailed analysis about the roots of this failure of unitarity. We investigate the impediments to a unitary implementation of the evolution by considering modifications to the dynamics. These modifications may be regarded as perturbations. We show in a precise manner why and where unitary implementability fails in our system, and prove that the obstructions are extremely sensitive to modifications in the Hamiltonian that dictates the time evolution of the symmetry-reduced model. We are able to characterize to a certain extent how far the model is from unitarity. Moreover, we demonstrate that the dynamics can actually be approximated as much as one wants by means of unitary transformations. |
Title: Length uncertainty in a gravity's rainbow formalism. Authors: Pablo Galán, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 72, 044019 (2005) Abstract: It is commonly accepted that the combination of quantum mechanics and general relativity gives rise to the emergence of a minimum uncertainty both in space and time. The arguments that support this conclusion are mainly based on perturbative approaches to the quantization, in which the gravitational interactions of the matter content are described as corrections to a classical background. In a recent paper, we analyzed the existence of a minimum time uncertainty in the framework of doubly special relativity. In this framework, the standard definition of the energy-momentum of particles is modified appealing to possible quantum gravitational effects, which are not necessarily perturbative. Demanding that this modification be completed into a canonical transformation determines the implementation of doubly special relativity in position space and leads to spacetime coordinates that depend on the energy-momentum of the particle. In the present work, we extend our analysis to the quantum length uncertainty. We show that, in generic cases, there actually exists a limit in the spatial resolution, both when the quantum evolution is described in terms of the auxiliary time corresponding to the Minkowski background or in terms of the physical time. These two kinds of evolutions can be understood as corresponding to perturbative and nonperturbative descriptions, respectively. This result contrasts with that found for the time uncertainty, which can be made to vanish in all models with unbounded physical energy if one adheres to a nonperturbative quantization. |
Title: Exact quantization of Einstein-Rosen waves coupled to massless scalar matter Authors: J. Fernando Barbero G., Iñaki Garay, and Eduardo J. S. Villaseñor Journal-ref: Phys.Rev.Lett.95 (2005) 051301 Abstract: We show in this letter that gravity coupled to a massless scalar field with full cylindrical symmetry can be exactly quantized by an extension of the techniques used in the quantization of Einstein-Rosen waves. This system provides a useful testbed to discuss a number of issues in quantum general relativity such as the emergence of the classical metric, microcausality, and large quantum gravity effects. It may also provide an appropriate framework to study gravitational critical phenomena from a quantum point of view, issues related to black hole evaporation, and the consistent definition of test fields and particles in quantum gravity. |
Title: Asymptotics of regulated field commutators for Einstein-Rosen waves. Authors: J.Fernando Barbero G., Guillermo A. Mena Marugán, Eduardo J. S. Villaseñor. Journal-ref: J. Math. Phys. 46, 062306 (2005) Abstract: We discuss the asymptotic behavior of regulated field commutators for linearly polarized, cylindrically symmetric gravitational waves and the mathematical techniques needed for this analysis. We concentrate our attention on the effects brought about by the introduction of a physical cutoff in the study of the microcausality of the model and describe how the different physically relevant regimes are affected by its presence. Specifically we discuss how genuine quantum gravity effects can be disentangled from those originating in the introduction of a regulator. |
Title: Quantum time uncertainty in a gravity's rainbow formalism. Authors: Pablo Galán, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 70, 124003 (2004) Abstract: The existence of a minimum time uncertainty is usually argued to be a consequence of the combination of quantum mechanics and general relativity. Most of the studies that point to this result are nonetheless based on perturbative quantization approaches, in which the effect of matter on the geometry is regarded as a correction to a classical background. In this paper, we consider rainbow spacetimes constructed from doubly special relativity by using a modification of the proposals of Magueijo and Smolin. In these models, gravitational effects are incorporated (at least to a certain extent) in the definition of the energy-momentum of particles without adhering to a perturbative treatment of the backreaction. In this context, we derive and compare the expressions of the time uncertainty in quantizations that use as evolution parameter either the background or the rainbow time coordinates. These two possibilities can be regarded as corresponding to perturbative and nonperturbative quantization schemes, respectively. We show that, while a nonvanishing time uncertainty is generically unavoidable in a perturbative framework, an infinite time resolution can in fact be achieved in a nonperturbative quantization for the whole family of doubly special relativity theories with unbounded physical energy. |
Title: Inner boundary conditions for black hole initial data derived from isolated horizons. Authors: José Luis Jaramillo, Eric Gourgoulhon, Guillermo A. Mena Marugán. Journal-ref: Phys. Rev. D 70, 124036 (2004) Abstract: We present a set of boundary conditions for solving the elliptic equations in the initial data problem for space-times containing a black hole, together with a number of constraints to be satisfied by the otherwise freely specifiable standard parameters of the conformal thin sandwich formulation. These conditions altogether are sufficient for the construction of a horizon that is instantaneously in equilibrium in the sense of the isolated horizons formalism. We then investigate the application of these conditions to the initial data problem of binary black holes and discuss the relation of our analysis with other proposals that exist in the literature. |
Title: Particles and vacuum for perturbative and non-perturbative Einstein-Rosen gravity. Authors: J.Fernando Barbero G., Guillermo A. Mena Marugán, Eduardo J. S. Villaseñor. Journal-ref: Phys. Rev. D 70, 044028 (2004) Abstract: We discuss the connection between the Fock space introduced by Ashtekar and Pierri for Einstein-Rosen waves and its perturbative counterpart based on the concept of a particle that arises in linearized gravity with a de Donder gauge. We show that the gauge adopted by Ashtekar and Pierri is indeed a generalization of the de Donder gauge to full (i.e., non-linearized) cylindrical gravity. This fact allows us to relate the two descriptions of the Einstein-Rosen waves analyzed here (the perturbative one and that made by Ashtekar and Pierri) by means of a simple field redefinition. Employing this redefinition, we find the highly non-linear relation that exists between the annihilation and creation-like variables of the two approaches. We next represent the particle-like variables of the perturbative approach as regularized operators, introducing a cutoff. These can be expanded in powers of the annihilation and creation operators of the Ashtekar-Pierri quantization, each additional power being multiplied by an extra square root of (h times) the three-dimensional gravitational constant, sqrt[G]. In principle, the perturbative vacuum may be reached as the limit of a state annihilated by these regularized operators when the cutoff is removed. This state can be written as the vacuum of the Ashtekar-Pierri quantization corrected by a perturbative series in sqrt[G] with no contributions from particles with energies above the cutoff. We show that the first-order correction is in fact a state of infinite norm. This result is interpreted as indicating that the Fock quantizations in the two approaches are unitarily inequivalent and, in any case, proves that the perturbative vacuum is not analytic in the interaction constant. Therefore a standard perturbative quantum analysis fails. |
Title: Asymptotic analysis of field commutators for Einstein-Rosen gravitational waves. Authors: J.Fernando Barbero G., Guillermo A. Mena Marugán, Eduardo J. S. Villaseñor. Journal-ref: J. Math. Phys. 45, 3498 (2004) Abstract: We give a detailed study of the asymptotic behavior of field commutators for linearly polarized, cylindrically symmetric gravitational waves in different physically relevant regimes. We also discuss the necessary mathematical tools to carry out our analysis. Field commutators are used here to analyze microcausality, in particular the smearing of light cones owing to quantum effects. We discuss in detail several issues related to the semiclassical limit of quantum gravity, in the simplified setting of the cylindrical symmetry reduction considered here. We show, for example, that the small G behavior is not uniform in the sense that its functional form depends on the causal relationship between spacetime points. We consider several physical issues relevant for this type of models such as the emergence of large gravitational effects. |
Title: Quantum cylindrical waves and sigma models. Authors: J.Fernando Barbero G., Guillermo A. Mena Marugán, Eduardo J. S. Villaseñor. Journal-ref: Int. J. Mod. Phys. D 13, 1119 (2004) Abstract: We analyze cylindrical gravitational waves in vacuo with general polarization and develop a viewpoint complementary to that presented recently by Niedermaier showing that the auxiliary sigma model associated with this family of waves is not renormalizable in the standard perturbative sense. |
Title: Time uncertainty in quantum gravitational systems Authors: J. Fernando Barbero G., Guillermo A. Mena Marugan, and Eduardo J. S. Villaseñor Journal-ref: Phys.Rev.D69 (2004) 044017 Abstract: It is generally argued that the combined effect of the Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We consider a simple family of gravitational models, including the Einstein-Rosen waves, in which the (nonlinearized) inclusion of gravity changes the normalization of time translations by a monotonic energy-dependent factor. In these circumstances, it is shown that a maximum time resolution emerges nonperturbatively only if the total energy is bounded. Perturbatively, however, there always exists a minimum uncertainty in the physical time. |