arXiv subjects

Alice Boldrin

Publications and source records attributed to Alice Boldrin.

6 recordsLinked to original sources

arXiv2026

Generalized relative locality and causal sets

In this paper we introduce a new general framework for the study of phenomenological quantum gravity theories (PQG). The key idea is the introduction of two different types of spacetime, an observer-independent spacetime (modeled by a smooth orientable manifold) and an observer-dependent one (which has an inherently discrete causal set structure). The interaction between the two allows us to prove the main result of the paper: relative locality can be obtained in general PQG models, regardless of momentum-space curvature. {We also discuss the treatment of spacetime symmetries in our model, and introduce a direct link between spacetime symmetries and relative locality effects.} Our construction is presented in a coordinate-independent way and is based on fibre bundles where spacetime, rather than momentum-space, is the base manifold. This makes causality manifest even in general models with relative locality. Furthermore, it allows for the application of this formalism to cosmology on general backgrounds, something which is not clearly possible in the canonical approach to relative locality, where momentum-space serves as the base manifold.

gr-qc↗

arXiv2025

Classical and quantum aspects of perturbations in Primordial Universe

In this work, our aim is to obtain a Hamiltonian formulation suitable for canonical quantization. Moreover, we assume that the early Universe can be described with fewer initial symmetries, thus we abandon the isotropy assumption and instead explore anisotropic universes, beginning with the simplest one, namely Bianchi I (BI). The presence of small initial fluctuations in the early universe can be well described by perturbations around a homogeneous background. GR is a constrained system, and we apply the so-called Dirac procedure for constrained systems to derive a gauge-invariant Hamiltonian formulation suitable for quantization. In this work, we present how this procedure can be extended to a generic background and its relation to the Kuchar decomposition. Subsequently, we apply this formulation to a BI universe, obtaining new and interesting results on the gauge-invariant representation of matter and geometry perturbations. Contrary to the FLRW case, in which all the modes decouple, in BI we see that scalar and tensor modes do not decouple. We show that new types of gauge-fixing conditions exit in this case. For instance, a gravitational wave can be encoded into scalar modes, by introducing a new gauge which is not valid in FLRW. Furthermore, we make a first step towards a consistent and unified quantization of the composite system made of a background mode and perturbation modes. Specifically, we study tensor modes in a FLRW universe. We focus on the relation between the choice of internal time of the universe and the quantum evolution it undergoes. Our results indicate that the time reparametrization invariance in general relativity affects the quantum evolution of the background and perturbation modes. However, in the classical limit, i.e. for a large universe, the dynamics becomes unique. Thus, the predictive power of the theory is maintained.

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arXiv2024

Time problem in primordial perturbations

We study the non-unitary relation between quantum gravitational models defined using different internal times. We show that despite the non-unitarity, it is possible to provide a prescription for making unambiguous, though restricted, physical predictions independent of specific clocks. To illustrate this result, we employ a model of quantum gravitational waves in a quantum Friedmann universe.

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arXiv2023

The Gauge issue and the Hamiltonian theory of cosmological perturbations

We present a general formalism for the Hamiltonian description of perturbation theory around any spatially homogeneous spacetime. We employ and refine the Dirac method for constrained systems, which is very well-suited to cosmological perturbations. This approach includes a discussion of the gauge-invariant dynamics of perturbations as well as an analysis of gauge transformations, gauge-fixing, partial gauge-fixing and spacetime reconstruction. We will introduce the Kucha\v{r} parametrization of the kinematical phase space as a convenient tool for studying the gauge transformations. The key element of this approach is the reconstruction of spacetime based on gauge-fixing conditions.

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arXiv2022

Gauge-fixing and spacetime reconstruction in the Hamiltonian theory of cosmological perturbations

We develop a complete Hamiltonian approach to the theory of perturbations around any spatially homogeneous spacetime. We employ the Dirac method for constrained systems which is well-suited to cosmological perturbations. We refine the method via the so-called Kucha\vr parametrization of the kinematical phase space. We separate the gauge-invariant dynamics of the three-surfaces from the three-surface deformations induced by linear coordinate transformations. The canonical group of the three-surface deformations and the complete space of gauge-fixing conditions are explicit in our approach. We introduce a frame in the space of gauge-fixing conditions and use it to considerably simplify the prescription for gauge-fixing, partial gauge-fixing and spacetime reconstruction. Finally, we illustrate our approach by considering the perturbed Kasner universe, for which we discuss two kinds of gauges that correspond respectively to the Coulomb-like and the Lorenz-like gauge in electrodynamics.

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arXiv2021

Dirac procedure and the Hamiltonian formalism for cosmological perturbations in a Bianchi I universe

We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Bianchi I universe. We discuss and employ basic concepts such as Dirac observables, Dirac brackets, gauge-fixing conditions, reduced phase space, physical Hamiltonian, canonical isomorphism between different gauge-fixing surfaces and spacetime reconstruction. We relate this approach to the gauge-fixing procedure for non-perturbative canonical relativity. We discuss the issue of propagating a basis for the scalar-vector-tensor decomposition as, in an anisotropic universe, the wavefronts of plane waves undergo a nontrivial evolution. We show that the definition of a gravitational wave as a traceless-transverse mode of the metric perturbation needs to be revised. Moreover there exist coordinate systems in which a polarization mode of the gravitational wave is given entirely in terms of a scalar metric perturbation. We first develop the formalism for the universe with a single scalar field and then extend it to the multi-field case. The obtained fully canonical formalism will serve as a starting point for a complete quantization of the cosmological perturbations and the cosmological background.

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