The vacuum state in hybrid loop quantum cosmology
Title (trans.)
El estado de vacío en cosmología cuántica de lazos híbridaAuthor
Prado Loy, SantiagoEntity
UAM. Departamento de Física TeóricaDate
2022-05-27Subjects
Vacío (Física); Teoría cuántica; FísicaNote
Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de Lectura: 27-05-2022Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
In generic curved spacetimes, the absence of a natural vacuum state introduces an ambiguity
that can undermine the physical relevance of predictions from any field quantization. In the context
of inhomogeneous fields propagating in homogeneous, isotropic, but otherwise general cosmological
spacetimes, this problem obstructs the extraction of robust predictions. This obstruction is aggravated
in applications to cosmology of candidates to a quantum theory of gravity, where even the
cosmological background where the fields propagate is treated as a quantum entity, or at most as
an effective spacetime. One example is provided by the hybrid approach to quantum cosmology, in
which a quantum mechanical description of the cosmological degrees of freedom, usually within Loop
Quantum Cosmology (LQC), is combined with a more conventional Fock quantization of the infinite
number of degrees of freedom that account for the inhomogeneities. In this context, we investigate
in this thesis physical criteria to successfully remove the ambiguity of choice of vacuum state for
two different types of fields in hybrid LQC: fermionic fields treated as perturbations, and primordial
scalar and tensor perturbations leading to non-oscillating (NO) power spectra. For fermions, we first
restrict ourselves to a family of vacua which leads to a unitarily implementable quantum Heisenberg
evolution. Then, we manage to further restrict this choice by considering the asymptotic limit of
large Fourier wavenumbers in the mode decomposition of the Dirac field and demanding there a convergent
quantum backreaction. Further restrictions in this limit also guarantee that the fermionic
contribution to the Hamiltonian be a well defined quantum operator on the dense subset of the
fermionic Fock space which is spanned by the n-particle/antiparticle states. Finally, we use the entire
available asymptotic freedom in what respects the definition of a vacuum state to eliminate from
the fermionic Hamiltonian any term which creates or annihilates pairs of particles, at any given order
in the asymptotic limit. We compare the vacuum selected by these physical criteria with fermionic
adiabatic states, which had previously been proposed as potential vacua in cosmology. Actually, we
prove that all adiabatic states allow a unitarily implementable quantum evolution. Furthermore, all
of them but the zeroth order adiabatic state give rise to a finite backreaction. To finish our study of
the fermionic vacuum, we apply the suggested asymptotic diagonalization procedure in a de Sitter
Universe, showing that it picks out a unique vacuum state, which in fact coincides with the wellknown
Bunch-davies vacuum. In addition to the problem of fermions in cosmology, we also discuss
the possible choice of a vacuum state for scalar and tensor cosmological perturbations in LQC by
demanding an NO power spectrum. This type of NO vacuum was originally introduced by numeric
means to avoid the rapid oscillations in the spectrum found in the literature for other states of the
perturbations, oscillations that could result in an amplification of power when averaged over bins of
Fourier wavenumbers. We provide some analytic insights into why these oscillations may in fact be
an artifact of the choice of vacuum state and how they can blur the actual quantum geometry effects
in observational predictions if they are not avoided. We also give some analytical conditions that are
necessary on a vacuum state if it is of NO type, and prove that in the ultraviolet asymptotic limit this
class of vacua satisfy the asymptotic diagonalization proposal. Finally, we compare these necessary
NO conditions with a construction for the vacuum put forward recently by Ashtekar and Gupt. This
construction should select the state which is maximally classic at the end of inflation from a ball of
states that is picked out by the so-called Quantum Homogeneity and Isotropy Hypothesis (QHIH).
However, we find a loose step in the proposed construction which allows that the Ashtekar-Gupt
vacuum to exist outside of the QHIH ball. In fact, we prove numerically that, in a kinetically dominated
short-lived inflationary scenario typically considered in LQC, the Ashtekar-Gupt vacuum lies
outside of the QHIH ball. Nonetheless, we show that the NO necessary conditions and the QHIH
are mutually non-exclusive in this scenario
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