arXiv subjects

Guillermo A. Mena Marugán

Publications and source records attributed to Guillermo A. Mena Marugán.

At least 19 recordsLinked to original sources

arXiv2026

Robustness of the primordial power spectrum in hybrid loop quantum cosmology to approximations near the bounce

We prove the robustness of the analytic approximation used in (hybrid) loop quantum cosmology to compute the primordial power spectrum of the cosmological perturbations for a recently proposed vacuum state (the non-oscillatory state with asymptotic Hamiltonian diagonalization). To investigate this, we study different approximations to the effective mass of these perturbations near the bounce, showing that the Pöschl-Teller potential employed in previous works leads to indistinguishable power spectra compared to other estimations of the mass, provided that they successfully capture the characteristic scale of the bounce, which translates into a scale of power suppression.

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arXiv2026

Quasinormal modes in effective loop quantum gravity and consequences for isospectrality

We investigate the quasinormal mode spectra of axial and polar perturbations about the effective Ashtekar, Olmedo, and Singh black hole geometry within the hybrid approach to loop quantum gravity. We also compare our results with those previously obtained by del-Corral and Olmedo for the dressed metric approach. Starting from mode equations that are straightforward effective counterparts of the classical equations, we compute these spectra by means of a high-order WKB method with Padé resummation. The violation of isospectrality between axial and polar perturbations that was claimed to exist in the dressed metric approach persists with the hybrid quantization, with deviations of the same order of magnitude as in the former effective case, although slightly larger for the hybrid prescription. In both situations, the isospectrality breaking decreases with the cubic root of the squared black hole mass in Planck units, consistently recovering the classical Schwarzschild limit. In addition, we perform a careful assessment of the applicability of the WKB approximation to the present effective analysis, confirming the parameter regions where the method remains reliable and highlighting specific mode cases for which the approximation breaks down.

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arXiv2026

Hamiltonian formalism, master functions and Darboux transformations for perturbed (interiors and exteriors of) nonrotating black holes

Motivated by their relevance to the interior of nonrotating black holes, classical and quantum Kantowski-Sachs cosmologies have recently attracted increasing attention. This interest has led to the development of a Hamiltonian formalism for axial and polar perturbations, which can be extended to applications in the exterior region. The formalism provides also a description of the background physical degrees of freedom. Moreover, it allows for the construction of all physical perturbative gauge invariants, which can be arranged into canonical pairs associated with master functions. In this work, we review the basis of this Hamiltonian formalism, putting the emphasis on its foundations and fundamental steps rather than on details of the involved calculations. Our discussion focuses on classical and effective aspects, although we also briefly comment on its natural role in the quantization of perturbed black holes. Adopting this formalism we present a geometric interpretation of Darboux transformations between pairs of master functions, characterizing them as generalized canonical transformations that preserve the Hamiltonian structure of the perturbations as harmonic oscillators subject to certain potentials. This bijective correspondence between such canonical transformations and Darboux transformations, which was recently proved to hold for axial perturbations, is here extended to the case of polar perturbations. In addition, we demonstrate the existence of canonical transformations that, similarly to Darboux transformations, mix axial and polar master functions.

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arXiv2026

Parametrization of the primordial power spectrum in loop quantum cosmology

We investigate the imprints on the angular power spectra of cosmological perturbations of a pre-inflationary bounce phase, as described by the hybrid and dressed metric approaches to loop quantum cosmology. For this purpose, we derive a new parametrization of the primordial power spectrum at the end of the inflationary regime. Apart from slow-roll coefficients and cosmological parameters that are present in the standard cosmological scenario without quantum modifications, this parametrization additionally depends only on pre-inflationary physics. More specifically, we find a dependence on the number of e-folds during the bounce epoch and on a characteristic suppression scale which, given the e-folds accumulated during cosmic evolution, is determined by the energy density at the bounce. Recall that this density depends on the Immirzi parameter and the area gap known from LQG. This leads to a robust and accurate parametrization of the primordial power spectrum. Since in pre-inflationary scenarios there is no preferred vacuum state, we adopt the NO-AHD proposal, which selects a vacuum that is optimally adapted to the background dynamics and yields a non-oscillatory primordial power spectrum. With this choice, we show that the tensor-to-scalar ratio in both quantization approaches coincides with its expression in the standard $Λ$CDM model when the observed scales are not much smaller than the power-suppressed region. Computing also the angular power spectrum, we find that, for a total cosmic expansion of about 140 e-folds, both the hybrid and the dressed metric approaches exhibit excellent agreement with Planck data at high multipoles, while apparently improving the fit with respect to $Λ$CDM for low multipole numbers.

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arXiv2026

Master variables and Darboux symmetry for axial perturbations of the exterior and interior of black hole spacetimes

Recent efforts have shown that Kantowski-Sachs spacetime provides a useful framework for analyzing perturbations inside a Schwarzschild black hole (BH). In these studies, the adoption of a Hamiltonian formulation offers an insightful perspective. The aim of this work is twofold. First, we revisit and elaborate the results obtained so far in Kantowski-Sachs, with the focus placed on axial perturbations. In particular, by exploiting the relation between this spacetime and the interior of a nonrotating BH, we consider the extension of those results to the exterior geometry of the BH. In this way, we clarify the relation between the axial perturbative gauge invariants emerging from the canonical analysis and the already well-established axial BH invariants, often referred to as master functions. We do so by providing a unified picture of the Hamiltonian formalism, which does not distinguish, formally, between exterior and interior geometries. The second objective is to explore the role of Darboux transformations, which were found as hidden symmetries in the context of BH perturbations, and their appearance in the Hamiltonian setting. Within this framework, the Hamiltonian formulation provides a clear geometric interpretation and characterization of Darboux transformations within the axial sector, viewing them as the set of canonical transformations between Hamiltonians for axial master functions.

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arXiv2025

Expansion-sensitive coupling of a local quantum system in de Sitter cosmology

When a local quantum system couples to a quantum field in a cosmological spacetime, the time dependence of the coupling strength is conventionally taken to reflect the design of the local quantum system but not to depend on the large-scale structure of the universe. In this paper, we consider a novel coupling that incorporates additional time dependence that reflects the cosmological expansion, as motivated by structures that appear in quantum cosmology. We focus on a conformal scalar field in a de Sitter Friedmann-Lema\^ıtre-Robertson-Walker cosmology with flat but compact spatial sections in 3+1 dimensions, and a comoving Unruh-DeWitt detector: the novel coupling posits the detector to couple to the scaled scalar field that appears in the conformally related static spacetime. We survey the differences between the conventional and novel coupling, for detectors that couple to the full field and detectors that couple only to specific field modes, and for detectors with proper time internal dynamics and detectors with conformal time internal dynamics. We also briefly discuss noncompact spatial sections and single-mode detectors with discontinuous time dependence. We find that the novel coupling tends to enhance the de-excitation peaks in the detector's response, particularly for single-mode detectors.

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arXiv2025

Master functions and hybrid quantization of perturbed nonrotating black hole interiors

Master functions of black holes are fundamental tools in gravitational-wave physics and are typically derived within a Lagrangian framework. Starting from the Kantowski-Sachs geometry, one can instead construct a perturbative Hamiltonian description for the interior region of an uncharged and nonrotating black hole. This approach provides a complementary perspective and enables a quantum treatment of the background geometry and its perturbations. In this work, we extend the application of this formulation to the exterior region and establish a correspondence between the perturbative invariants of the canonical approach and the master functions commonly used in black hole analyses. Once a consistent Hamiltonian description for their canonical counterparts is obtained, a hybrid quantization of the master functions follows naturally.

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arXiv2025

Computing the graph-changing dynamics of loop quantum gravity

In loop quantum gravity (LQG), states of the gravitational field are represented by labeled graphs called spin networks. Their dynamics can be described by a Hamiltonian constraint, { which acts on the spin network states modifying both spins and graphs.} Fixed-graph approximations of the dynamics have been extensively studied, but its full graph-changing action so far remains elusive. The latter, alongside the solutions of its constraint, are arguably the missing features { in canonical LQG to access phenomenology in all its richness}. Here, we discuss a recently developed numerical tool that, for the first time, implements graph-changing dynamics via the Hamiltonian constraint. We explain how it is used to find new solutions to that constraint and to show that some quantum geometric observables behave differently than in the graph-preserving truncation. We also point out that these new numerical methods can find applications in other domains.

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arXiv2025

Starobinsky potential and power suppression in hybrid Loop Quantum Cosmology

We study the effect on the primordial tensor power spectrum of varying the number of e-folds during slow-roll inflation in Loop Quantum Cosmology with a Starobinsky potential. Using the hybrid quantization approach, we derive the effective mass governing tensor mode evolution. The choice of vacuum state is crucial, especially since the preinflationary phase predicted by Loop Quantum Cosmology invalidates the choice of the Bunch-Davies state as the preferred vacuum. We adopt a choice which is optimally adapted to the dynamics, so that it provides a non-oscillating (NO) spectrum free of spurious contributions, and permits an asymptotic Hamiltonian diagonalization (AHD) of the perturbations. For this so-called NO-AHD vacuum, we compute the power spectrum using both analytic approximations and numerical integration. Our results confirm the accuracy of our approximations in a wide range of situations, including short- and long-lived inflationary scenarios. The primordial power spectrum exhibits a characteristic cutoff on a wavenumber scale determined primarily by the background dynamics around the bounce that replaces the big bang in Loop Quantum Cosmology.

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arXiv2025

Taming Thiemann's Hamiltonian constraint in canonical loop quantum gravity: reversibility, eigenstates and graph-change analysis

The Hamiltonian constraint remains an elusive object in loop quantum gravity because its action on spinnetworks leads to changes in their corresponding graphs. As a result, calculations in loop quantum gravity are often considered unpractical, and neither the eigenstates of the Hamiltonian constraint, which form the physical space of states, nor the concrete effect of its graph-changing character on observables are entirely known. Much worse, there is no reference value to judge whether the commonly adopted graph-preserving approximations lead to results anywhere close to the non-approximated dynamics. Our work sheds light on many of these issues, by devising a new numerical tool that allows us to implement the action of the Hamiltonian constraint without the need for approximations and to calculate expectation values for geometric observables. To achieve that, we fill the theoretical gap left in the derivations of the action of the Hamiltonian constraint on spinnetworks: we provide the first complete derivation of such action for the case of 4-valent spinnetworks, while updating the corresponding derivation for 3-valent spinnetworks. Our derivations also include the action of the volume operator. By proposing a new approach to encode spinnetworks into functions of lists and the derived formulas into functionals, we implement both the Hamiltonian constraint and the volume operator numerically. We are able to transform spinnetworks with graph-changing dynamics perturbatively and verify that volume expectation values have rather different behavior from the approximated, graph-preserving results. Furthermore, using our tool we find a family of potentially relevant solutions of the Hamiltonian constraint. Our work paves the way to a new generation of calculations in loop quantum gravity, in which graph-changing results and their phenomenology can finally be accounted for and understood.

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arXiv2025

Polar perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology

Increasing attention has been recently devoted to the study of Kantowski-Sachs spacetime as a way to explore the interior of a Schwarzschild black hole. In this work, we construct a Hamiltonian formulation for polar perturbations of this spacetime in the presence of a perturbative massless scalar field. Our analysis is based on a truncated action at quadratic order in perturbations. Both background and perturbative degrees of freedom are treated dynamically, forming a combined system that is endowed with the canonical structure obtained from our truncated action. First-order perturbations of the metric and the matter field are described using perturbative gauge invariants, linear perturbative constraints, and their corresponding canonical variables. For the quantum description, we adopt a hybrid approach where the background is quantized with loop quantum gravity techniques and the perturbations with conventional quantum field methods.

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arXiv2025

Primodial power spectrum in loop quantum cosmology for different regularizations

In Loop Quantum Cosmology, the quantization of the Hamiltonian constraint involves a regularization procedure which is affected by certain ambiguities. Moreover, different regularizations lead to distinct mathematical formulations and, consequently, to different physical predictions. In this work, we explore the impact of this regularization on the primordial power spectrum of cosmological perturbations. More specifically, we study this power spectrum for the conventional regularization used in Loop Quantum Cosmology and for two alternative prescriptions suggested in the literature. We set initial conditions for the perturbations at the bounce corresponding to a recently proposed vacuum state, optimally adapted to the background dynamics. This choice of vacuum is based on an asymptotic Hamiltonian diagonalization in the ultraviolet sector of the perturbations which provides a non-oscillating power spectrum. Employing a suitable approximation to the propagation equations of the perturbations around the bounce, we are able to obtain an analytic expression for the primordial power spectrum of this vacuum for all the discussed regularizations. We compare the results and prove that the main relevant distinction between the corresponding spectra is the scale where power suppression occurs. The associated wavenumber scale is proportional to the square root of the critical density in Loop Quantum Cosmology, density which is different for each of the studied regularizations.

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arXiv2024

Choice of vacuum state and the relation between inflationary and Planck scales

Recent observations about the cosmic microwave background evidence a clear discrepancy between the scale of inflation and the Planck scale expected in the conventional inflationary picture, based on simple chaotic inflationary models. This paper explores a possible resolution of this conflict by considering a slight modification of the standard general relativity scenario, which naturally incorporates a cutoff scale consistent with the observations. This last scale of power suppression appears by the combined effect of the preinflationary background dynamics and an associated initial vacuum state for the cosmological perturbations which differs from the conventional Bunch-Davies state of slow-roll inflation. We revise and correct previous discussions in the literature about the relation between this scale and the scale corresponding to the onset of inflation. The mechanism that produces this cutoff is intimately related to the criterion determining a privileged vacuum state for the primordial perturbations. We adhere to a recent proposal based on an asymptotic diagonalization of the Hamiltonian of the perturbations and leading to a non-oscillatory primordial power spectrum. With this choice, we are able to investigate analytically the model, studying in detail some physically interesting cases. These analytic calculations provide further support to our arguments about the relation between the different scales of the system.

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arXiv2024

Comparing Analytic and Numerical Studies of Tensor Perturbations in Loop Quantum Cosmology

We investigate the implications of different quantization approaches in Loop Quantum Cosmology for the primordial power spectrum of tensor modes. Specifically, we consider the hybrid and dressed metric approaches to derive the effective mass that governs the evolution of the tensor modes. Our study comprehensively examines the two resulting effective masses and how to estimate them in order to obtain approximated analytic solutions to the tensor perturbation equations. Since Loop Quantum Cosmology incorporates preinflationary effects in the dynamics of the perturbations, we do not have at our disposal a standard choice of privileged vacuum, like the Bunch--Davies state in quasi-de Sitter inflation. We then select the vacuum state by a recently proposed criterion which removes unwanted oscillations in the power spectrum and guarantees an asymptotic diagonalization of the Hamiltonian in the ultraviolet. This vacuum is usually called the NO-AHD (from the initials of Non-Oscillating with Asymptotic Hamiltonian Diagonalization) vacuum. Consequently, we compute the power spectrum by using our analytic approximations and by introducing a suitable numerical procedure, adopting in both cases an NO-AHD vacuum. With this information, we compare the different spectra obtained from the hybrid and the dressed metric approaches, as well as from the analytic and numerical procedures. In particular, this proves the remarkable accuracy of our~approximations.

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arXiv2024

Analytic and Numerical Study of Scalar Perturbations in Loop Quantum Cosmology

The possibility that quantum geometry effects may alleviate the apparent tensions existing at large angular scales in the observations of the Cosmic Microwave Background explains the increasing interest in considering primordial perturbations within the framework of Loop Quantum Cosmology. In this framework, a number of approximations have been suggested to simplify the study of perturbations and derive analytic expressions for the power spectra. This study requires a new choice of vacuum state that takes into account the preinflationary background geometry, choice for which we adopt the so-called NO-AHD prescription. Here, we apply the aforementioned approximations to the investigation of scalar perturbations. We discuss two approaches to the quantization of perturbations in Loop Quantum Cosmology, namely the hybrid and the dressed metric approaches. We improve previous approximations by including slow-roll corrections in the inflationary era. Moreover, for the first time in the literature of the NO-AHD prescription, we compute numerically the primordial power spectra for the two considered approaches, and show that the analytic estimations are remarkably accurate for all observable modes. We also discuss the similarities and differences between the spectra obtained with those two approaches.

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arXiv2024

Axial perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology

Recently, there has been a growing interest in investigating homogeneous but anisotropic spacetimes owing to their relation with nonrotating, uncharged black hole interiors. We present a description of axial perturbations for a massless scalar field minimally coupled to this geometry. We truncate the action at the quadratic perturbative order and tailor our analysis to compact spatial sections. Perturbations are described in terms of perturbative gauge invariants, linear perturbative constraints, and their canonically conjugate variables. The entire set, encompassing perturbations and homogeneous degrees of freedom, is consolidated into a canonical one. We employ a hybrid approach to quantize this system, integrating a quantum representation of the homogeneous sector using Loop Quantum Cosmology techniques with a conventional field quantization of the perturbations.

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arXiv2024

Time-dependent scalings and Fock quantization of a massless scalar field in Kantowski-Sachs

We address the issue of inequivalent Fock representations in Quantum Field Theory in a curved homogenous and anisotropic background, namely Kantowski-Sachs spacetime. A family of unitarily equivalent Fock representations that are invariant under the spatial isometries and implement a unitary dynamics can be achieved by means of a field redefinition that consists of a specific anisotropic scaling of the field configuration and a linear transformation of its momentum. Remarkably, we show that this kind of field redefinition is in fact unique under our symmetry and unitary requirements. However, the physical properties of the Hamiltonian dynamics that one obtains in this way are not satisfactory, inasmuch as the action of the Hamiltonian on the corresponding particle states is ill defined. To construct a quantum theory without this problem, we need a further canonical transformation that is time- and mode-dependent and is not interpretable as an anisotropic scaling. The old and new Fock representations, nevertheless, are unitarily equivalent. The freedom that is introduced when allowing for this further canonical transformation can be fixed by demanding an asymptotic diagonalization of the Hamiltonian and a minimal absorption of dynamical phases. In this way, the choice of vacuum and the associated Fock representation are asymptotically determined.

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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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