arXiv subjects

Beatriz Elizaga Navascués

Publications and source records attributed to Beatriz Elizaga Navascués.

At least 19 recordsLinked to original sources

arXiv2026

Vacuum-purified Hawking radiation from evaporating black holes: Lessons from moving mirrors

This article investigates the possibility that Hawking-like quanta emitted by a moving mirror can be purified by late-time vacuum fluctuations, as proposed in Hotta, Schützhold and Unruh [Phys. Rev. D 91, 124060 (2015)]. Our motivation originates from recent discussions in Wald [Phys. Rev. D 100, 065019 (2019)] and Osawa et al. [Phys. Rev. D 110, 025023 (2024)] on whether vacuum purification necessarily entails a prohibitively large (indirect) energy cost, and our goal is to help clarify this issue. We identify the aspects of the mirror trajectory that determine the partners of Hawking quanta, as well as those that govern the energy carried to future null infinity. This allows us to highlight a fundamental disconnection within quantum field theory between the fluxes of quantum information (or purification) and energy. Throughout, we focus on quantities such as local correlation functions and energy fluxes, thereby avoiding reliance on a particle-based interpretation. Finally, we introduce an analytic mirror trajectory that produces Hawking radiation with an adiabatically varying temperature, mimicking the emission from an evaporating black hole. Our analysis identifies constraints on the mirror trajectory under which vacuum purification remains compatible with a prescribed energy budget, and we discuss the lessons that may be drawn from this model for realistic evaporating black holes.

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arXiv2026

Effective Regge-Wheeler equations of a hybrid loop quantum black hole

A set of effective equations for the gauge-invariant gravitational perturbations in the interior of a spherically symmetric, non-rotating black hole is derived within the framework of hybrid loop quantum cosmology. The quantum zero-mode of the Hamiltonian constraint, obtained from a perturbative gauge-invariant canonical analysis, is explicitly imposed on a class of quantum states whose wavefunctions factorize into a background and a perturbative part, related through a geometric relational variable. These states naturally describe regimes with small perturbative backreaction and lead to an effective Hamiltonian and associated dynamics for the perturbations. The resulting equations take the form of Regge-Wheeler equations modified by expectation values of the quantum black hole geometry, providing a clear characterization of quantum corrections to the classical description of the black hole interior. This framework opens the way to investigating hybrid loop quantum gravity effects in the propagation of gravitational waves.

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arXiv2024

Entangled pairs in evaporating black holes without event horizons

Investigations into Hawking radiation often assume a black hole model featuring an event horizon, despite the growing consensus that such causal structures may not exist in nature. While this assumption is not crucial for deriving the local properties of radiation at future null infinity, it plays a significant role in discussions about Hawking partners -- the field modes that purify Hawking radiation. This article aims to explore the definition and fate of Hawking partners in black hole scenarios where semiclassical mass loss due to Hawking radiation is considered. Our analysis avoids the assumption of event horizons and instead focuses on collapse processes that feature a trapped region bounded by a dynamical horizon. We derive the form of the partners, accounting for the effects of back-scattering. Furthermore, using these results and mild assumptions, we find that Hawking partners cannot "leak" out of the dynamical horizon to partially purify the Hawking radiation in the regime where general relativity coexists semiclassically with quantum field theory. This finding emphasizes the necessity for new physics, such as quantum gravity, to resolve the final fate of information.

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arXiv2024

On the evolution of the volume in Loop Quantum Cosmology

The dynamics of the expectation value of the volume is one of the key ingredients behind the replacement of the Big Bang singularity by a bounce in Loop Quantum Cosmology. As such, it is of great importance that this quantity is mathematically well-defined in the space of physical states of the theory. A number of caveats have been raised about such a definition entering in conflict with the quantum evolution of states, motivated by the situation found in quantum geometrodynamics. We show that there are ways around these caveats, all of which are related to the existence of quantization prescriptions leading to a nondegenerate curvature operator in Loop Quantum Cosmology. Interestingly, the properties of the curvature operator that may allow for a good behavior of the volume are only possible thanks to the discreteness of the geometry characteristic of the loop quantization procedure.

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arXiv2023

Effects of the inflaton potential on the primordial power spectrum in Loop Quantum Cosmology scenarios

In scenarios of physical interest in Loop Quantum Cosmology, with a preinflationary epoch where the kinetic energy of the inflaton dominates, the analytic study of the dynamics of the primordial fluctuations has been carried out by neglecting the inflaton potential in those stages of the evolution. In this work we develop approximations to investigate the influence of the potential as the period of kinetic dominance gives way to the inflationary regime, treating the potential as a perturbation. Specifically, we study how the potential modifies the effective mass that dictates the dynamics of the scalar perturbations in the preinflationary epochs, within the framework of the so-called hybrid prescription for Loop Quantum Cosmology. Moreover, we motivate and model a transition period that connects the kinetically dominated regime with inflation, allowing us to study the interval of times where the contribution of the potential is no longer negligible but an inflationary description is not yet valid. Finally, we include the main modifications coming from a slow-roll correction to a purely de Sitter evolution of the perturbations during inflation. We analytically solve the dynamics of the perturbations in each of these different epochs of cosmological evolution, starting from initial conditions fixed by the criterion of asymptotic Hamiltonian diagonalization. This enables us to compute and quantitatively analyze the primordial power spectrum in a specific case, using a quadratic inflaton potential.

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arXiv2023

Extended phase space quantization of a black hole interior model in Loop Quantum Cosmology

Considerable attention has been paid to the study of the quantum geometry of nonrotating black holes within the framework of Loop Quantum Cosmology. This interest has been reinvigorated since the introduction of a novel effective model by Ashtekar, Olmedo, and Singh. Despite recent advances in its foundation, there are certain questions about its quantization that still remain open. Here we complete this quantization taking as starting point an extended phase space formalism suggested by several authors, including the proposers of the model. Adopting a prescription that has proven successful in Loop Quantum Cosmology, we construct an operator representation of the Hamiltonian constraint. By searching for solutions to this constraint operator in a sufficiently large set of dual states, we show that it can be solved for a continuous range of the black hole mass. This fact seems in favour of a conventional classical limit (at least for large masses) and contrasts with recent works that advocate a discrete spectrum. We present an algorithm that determines the solutions in closed form. To build the corresponding physical Hilbert space and conclude the quantization, we carry out an asymptotic analysis of those solutions, which allows us to introduce a suitable inner product on them.

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arXiv2023

Fock quantization of a Klein-Gordon field in the interior geometry of a nonrotating black hole

We study the canonical quantization of a scalar field in a Kantowski-Sachs spacetime. For simplicity, we consider compactified spatial sections, since this does not affect the ultraviolet behavior. A time-dependent canonical transformation is performed prior to quantization. As in previously studied cases, the purpose of this canonical transformation is to identify and extract the background contribution to the field evolution which is obstructing a unitary implementation of the field dynamics at the quantum level. This splitting of the time dependence into a background piece and the part to be seen as true quantum evolution is to a large extent determined by the unitarity requirement itself. The quantization is performed in the usual setup of Fock representations, demanding the preservation of the spatial symmetries. Under the joint requirements of quantum unitary dynamics and compatibility with those classical symmetries, the quantization is shown to be unique, in the sense that any two representations with these properties are unitarily equivalent. This confirms the validity of our conditions as criteria to discriminate among possibly inequivalent quantum descriptions. The interest of this analysis goes beyond cosmological applications since the interior of a nonrotating black hole has a geometry of the Kantowski-Sachs type.

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arXiv2022

Space of solutions of the Ashtekar-Olmedo-Singh effective black hole model

We consider a general choice of integration constants in the resolution of the dynamical equations derived from a recently proposed effective model that describes black hole spacetimes in the context of loop quantum cosmology. The interest of our analysis is twofold. On the one hand, it allows for a study of the entire space of solutions of the model, which is absent in the literature and is fundamental for understanding the relation with any underlying quantum theory. On the other hand, choices of integration constants that generalize the type of solutions considered so far may lead to exotic behaviors in the effective black hole geometry, as well as modified thermodynamical properties. With these motivations in mind, we discuss the interior and exterior geometries, and present the conditions that a satisfactory matching at the horizons imposes. Then, we turn our attention to the Hawking temperature associated with the black horizon of the model, which we find to be affected by the freedom of choice of integration constants. Finally, we briefly comment on the asymptotic structure of the general solution and compare different notions of mass.

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arXiv2022

Hamiltonian formulation and loop quantization of a recent extension of the Kruskal spacetime

We study the Hamiltonian formulation of the Ashtekar-Olmedo-Singh model for the description of the interior geometry of non-rotating, uncharged black holes. This model incorporates loop quantum effects through the introduction of two regularization parameters. We consider an extended phase space formalism proposed by the creators of the model that includes such parameters as configuration variables, constrained to be functions of the black hole mass. We generalize this restriction, allowing for an off-shell phase space dependence. We then introduce a gauge fixing procedure and reduce the system, proving that the reduced symplectic structure cannot reproduce the standard relativistic one in terms of the densitized triad and the Ashtekar-Barbero connection. Actually, the reduced structure precisely compensates the modifications that arise in the Hamilton equations when the regularization parameters are treated as phase space functions, rather than as numbers, attaining a consistent Hamiltonian derivation of the dynamics. We then choose the extended phase space formalism as starting point to address the loop quantization of the model. Taking the definition of certain geometric operators as the only basic ingredient and adopting prescriptions that have proven successful in loop quantum cosmology, we construct a polymer representation of all the constraints and deduce the formal expression of the physical states, assuming reasonable spectral properties for the constraint operators. The physical states turn out to be characterized by a wave function of the black hole mass with support on a very specific set. We finally discuss conditions that guarantee the existence of physical states in the region of large black hole masses. This is a first step in the development of a new loop quantum theory of black holes.

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arXiv2021

Non-oscillating vacuum states and the quantum homogeneity and isotropy hypothesis in Loop Quantum Cosmology

We study the compatibility of the quantum homogeneitiy and isotropy hypothesis (QHIH), proposed by Ashtekar and Gupt to restrict the choice of vacuum state for the cosmological perturbations in Loop Quantum Cosmology (LQC), with the requirement that the selected vacuum should lead to a power spectrum that does not oscillate. We inspect in close detail the procedure that these authors followed to construct a set of states satisfying the QHIH, and how a preferred vacuum can be determined within this set. We find a step that is not univocally specified in this procedure, in relation with the replacement of the set of states that was originally allowed by the QHIH with an alternative set that is more manageable. In fact, the first of these sets does not contain the state that has been used in most of the implementations of the QHIH to the analysis of the power spectrum of the perturbations in LQC. We focus our attention on the original set picked out by the QHIH and investigate whether some of its elements may display a non-oscillatory behavior. We show that, to the extent to which the techniques used in this paper apply, this possibility is feasible. Thus, the two aforementioned criteria for the physical restriction of the vacuum state in LQC are compatible with each other and not exclusive.

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arXiv2021

Quantization ambiguities and the robustness of effective descriptions of primordial perturbations in hybrid Loop Quantum Cosmology

We study the imprint that certain quantization ambiguities may leave in effective regimes of the hybrid loop quantum description of cosmological perturbations. More specifically, in the case of scalar perturbations we investigate how to reconstruct the Mukhanov-Sasaki field in the effective regime of Loop Quantum Cosmology, taking as starting point for the quantization a canonical formulation in terms of other perturbative gauge invariants that possess different dynamics. This formulation of the quantum theory, in terms of variables other than the Mukhanov-Sasaki ones, is crucial to arrive at a quantum Hamiltonian with a good behavior, elluding the problems with ill defined Hamiltonian operators typical of quantum field theories. In the reconstruction of the Mukhanov-Sasaki field, we ask that the effective Mukhanov-Sasaki equations adopt a similar form and display the same Hamiltonian structure as the classical ones, a property that has been widely assumed in Loop Quantum Cosmology studies over the last decade. This condition actually restricts the freedom inherent to certain quantization ambiguities. Once these ambiguities are removed, the reconstruction of the Mukhanov-Sasaki field naturally identifies a set of positive-frequency solutions to the effective equations, and hence a choice of initial conditions for the perturbations. Our analysis constitutes an important and necessary test of the robustness of standard effective descriptions in Loop Quantum Cosmology, along with their observational predictions on the primordial power spectrum, taking into account that they should be the consequence of a more fundamental quantum theory with a well-defined Hamiltonian, in the spirit of Dirac's long-standing ideas.

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arXiv2021

Primordial perturbations in kinetically dominated regimes of general relativity and hybrid quantum cosmology

Scalar fields with an energy density dominated by its kinetic part may have played a relevant role in the very early stages of the Universe. Compared to the standard inflationary paradigm, they may lead to modifications in observable quantities, e.g. the anisotropies found in the cosmic microwave background. Kinetically dominated regimes arise in classical fast-roll scenarios as well as in quantum bouncing cosmologies. For instance, kinetic dominance is typical in interesting preinflationary phases of Loop Quantum Cosmology. In this work, we analyze the leading-order effects that the presence of a scalar field potential causes on the primordial cosmological perturbations in these kinetically dominated epochs. These effects can be grouped in two sets, namely, those that affect the effective mass of the perturbations and those that affect the choice of their vacuum state. The effective mass is modified directly by terms that include the potential, but also indirectly by the change in the background dynamics and the relation between the parameterization of these dynamics and the conformal time, usually employed to describe the evolution of the perturbations. On the other hand, away from de Sitter inflation, the Bunch-Davies state is no longer the most natural vacuum at all scales. Recent proposals suggest to modify it by carrying out certain Hamiltonian diagonalization with a suitable asymptotic behavior at large wavenumber scales. Both this diagonalization condition and the imposed asymptotic behavior depend on the effective mass of the perturbations, and therefore the selected vacuum state varies in the presence of the scalar field potential.

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arXiv2021

Perturbations in Quantum Cosmology: The Continuum Limit in Fourier Space

We analyze the passage to a continuum limit of the mode spectrum of primordial perturbations around flat cosmological spacetimes in Quantum Cosmology, showing that this limit can be reached even if one starts by considering a finite fiducial cell as spatial slice. Whereas the resulting system can be described in an invariant way under changes of the fiducial volume using appropriate variables, both for the background cosmology and the perturbations, obtaining in this way a discrete mode spectrum owing to the compactness of the fiducial cell, we show that the desired continuum limit for the perturbations can still be established by means of scaling transformations of the physical volume when this volume grows unboundedly. These transformations lead to a model with a continuum of modes and independent of any scale of reference for the physical volume. For the sake of comparison, we also consider an alternative road to the continuum in Fourier space that has been employed in geometrodynamics and is based on the use of scaling transformations of the fiducial volume, together with variables that are independent of them.

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arXiv2021

Analytical investigation of pre-inflationary effects in the primordial power spectrum: From General Relativity to hybrid Loop Quantum Cosmology

This work is an analytical study of the main differences between classical inflationary effects of a fast-roll regime and imprints of hybrid Loop Quantum Cosmology (LQC) on the primordial power spectrum. Effective LQC solutions of phenomenological interest typically contain a classical period of kinetic dominance prior to slow-roll inflation, with consequences on the power spectrum that here we try and tell apart from those of phenomena occuring in the vicinity of a bounce in hybrid LQC. For this comparison, we use the same criterion for the choice of a vacuum state of the primordial perturbations, both in the context of relativistic cosmology and on the LQC cosmological background. As a first approximation to the problem, our study ignores the influence of a quasi-de Sitter evolution (rather than de Sitter) in the slow-roll inflationary regime, and of a typically short transition between the kinetically dominated era and the slow-roll period. Our results show that, while the two studied types of effects can lead to a drastic power suppression in the infrared sector of the spectrum, the mode scale at which this happens is much larger for LQC than for classical relativistic cosmology, the corresponding scales being related to the spacetime curvature at the bounce and at the onset of inflation, respectively.

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arXiv2021

Hybrid Loop Quantum Cosmology: An Overview

Loop Quantum Gravity is a nonperturbative and background independent program for the quantization of General Relativity. Its underlying formalism has been applied successfully to the study of cosmological spacetimes, both to test the principles and techniques of the theory and to discuss its physical consequences. These applications have opened a new area of research known as Loop Quantum Cosmology. The hybrid approach addresses the quantization of cosmological systems that include fields. This proposal combines the description of a finite number of degrees of freedom using Loop Quantum Cosmology, typically corresponding to a homogeneous background, and a Fock quantization of the field content of the model. In this review we first present a summary of the foundations of homogeneous Loop Quantum Cosmology and we then revisit the hybrid quantization approach, applying it to the study of Gowdy spacetimes with linearly polarized gravitational waves on toroidal spatial sections, and to the analysis of cosmological perturbations in preinflationary and inflationary stages of the Universe. The main challenge is to extract predictions about quantum geometry effects that eventually might be confronted with cosmological observations. This is the first extensive review of the hybrid approach in the literature on Loop Quantum Cosmology.

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arXiv2021

Uniqueness Criteria for the Fock Quantization of Dirac Fields and Applications in Hybrid Loop Quantum Cosmology

In generic curved spacetimes, the unavailability of a natural choice of vacuum state introduces a serious ambiguity in the Fock quantization of fields. In this review, we study the case of fermions described by a Dirac field in several cosmological spacetimes, and present recent results about well-motivated criteria that ensure the uniqueness in the selection of a vacuum up to unitary transformations. These criteria are based on two requirements. First, the invariance of the vacuum under the symmetries of the Dirac equations in the considered spacetime. Second, the unitary implementability of the Heisenberg dynamics of the annihilation and creation operators when the curved spacetime is treated as a fixed background. This last requirement not only permits the uniqueness of the Fock quantization but, remarkably, it also determines an essentially unique splitting between the phase space variables assigned to the background and the fermionic annihilation and creation variables. We first consider Dirac fields in cosmological spacetimes of 2+1 dimensions and then discuss the more relevant case of 3+1 dimensions. We use this analysis to investigate the hybrid loop quantization of a flat Friedmann-Lemaître-Robertson-Walker background cosmology coupled to a perturbative Dirac field. Among the Fock quantizations for the fermionic perturbations allowed by our criteria, we further restrict the choice of vacuum by demanding a finite fermionic backreaction and, moreover, by diagonalizing the fermionic contribution to the total Hamiltonian in the asymptotic limit of large wave numbers of the Dirac modes. Finally, we argue in support of the uniquess of the vacuum state selected by the extension of this diagonalization condition beyond the ultraviolet regime, proving that it picks out the standard Poincaré and Bunch-Davies vacua for fixed flat and de Sitter background spacetimes, respectively.

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arXiv2021

Non-oscillating power spectra in Loop Quantum Cosmology

We characterize in an analytical way the general conditions that a choice of vacuum state for the cosmological perturbations must satisfy to lead to a power spectrum with no scale-dependent oscillations over time. In particular, we pay special attention to the case of cosmological backgrounds governed by effective Loop Quantum Cosmology and in which the Einsteinian branch after the bounce suffers a pre-inationary period of deccelerated expansion. This is the case more often studied in the literature because of the physical interest of the resulting predictions. In this context, we argue that non-oscillating power spectra are optimal to gain observational access to those regimes near the bounce where Loop Quantum Cosmology effects are non-negligible. In addition, we show that non-oscillatory spectra can indeed be consistently obtained when the evolution of the perturbations is ruled by the hyperbolic equations derived in the hybrid loop quantization approach. Moreover, in the ultraviolet regime of short wavelength scales we prove that there exists a unique asymptotic expansion of the power spectrum that displays no scale-dependent oscillations over time. This expansion would pick out the natural Poincaré and Bunch Davies vacua in Minkowski and de Sitter spacetimes, respectively, and provides an appealing candidate for the choice of a vacuum for the perturbations in Loop Quantum Cosmology based on physical motivations.

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arXiv2020

Unique fermionic vacuum in de Sitter spacetime from hybrid quantum cosmology

In this work we show how the criterion of asymptotic Hamiltonian diagonalization originated in hybrid quantum cosmology serves to pick out a unique vacuum for the Dirac field in de Sitter, in the context of quantum field theory in curved spacetimes. This criterion is based on the dynamical definition of annihilation and creationlike variables for the fermionic field, which obey the linearized dynamics of a Hamiltonian that has been diagonalized in a way that is adapted to its local spatial structure. This leads to fermionic variables that possess a precise asymptotic expansion in the ultraviolet limit of large wavenumbers. We explicitly show that, when the cosmological background is fixed as a de Sitter solution, this expansion uniquely selects the choice of fermionic annihilation and creationlike variables for all spatial scales, and thus picks out a unique privileged Fock representation and vacuum state for the Dirac field in de Sitter. The explicit form of the basis of solutions to the Dirac equation associated with this vacuum is then computed.

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