Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology

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.Comment: 11 pages, version accepted for publication in Physical Review

Perturbaciones primordiales en Cosmología Cuántica de Lazos

Las propiedades de homogeneidad e isotropía observadas en nuestro Universo sugieren que sus inhomogeneidades pueden ser tratadas como perturbaciones en torno a un espaciotiempo de fondo de tipo Friedmann-Lemaître-Robertson-Walker (FLRW). A decir verdad, la teoría de perturbaciones cosmológicas, combinada con el paradigma inflacionario, ofrece una buena aproximación a las anisotropías del fondo cósmico de microondas, y es capaz de explicar de manera bastante satisfactoria la formación de estructuras a escalas cosmológicas. El objetivo principal de esta tesis es proporcionar un marco sólido para la descripción cuántica de la evolución de las perturbaciones cosmológicas escalares (y, por extensión, también de las perturbaciones tensoriales) en el Universo Primitivo. Este marco, además, permite extraer predicciones, en la esperanza de poder contrastar los modelos teóricos con las observaciones, gracias a los recientes desarrollos técnicos que nos proporcionan datos cada vez con mayor precisión. Con el fin de investigar la posibilidad de encontrar información acerca de la verdadera naturaleza cuántica de la geometría del espacio-tiempo codificada en las huellas dejadas por las fluctuaciones cuánticas del Universo Primitivo, nuestro modelo debe involucrar, al mismo tiempo, tanto la geometría de fondo como las perturbaciones cosmológicas, interactuando entre sí. En esta tesis, elaboramos un programa de cuantización basado en un formalismo híbrido, que fue propuesto originalmente para la cuantización de los primeros modelos gravitacionales inhomogéneos que se estudiaron en Cosmología Cuántica de Lazos. La estrategia consiste en dividir el espacio de fases del sistema cosmológico considerado en dos: un sector homogéneo y otro inhomogéneo. Para ello, se realiza una expansión en modos de la métrica y el campo material, utilizando las simetrías espaciales. El sector homogéneo incorpora los modos cero, mientras que el inhomogéneo incluye el resto de grados de libertad presentes en las perturbaciones. A continuación, se combinan diferentes tipos de representaciones cuánticas para cada una de esas partes. En el grueso de nuestra discusión, utilizamos una cuantización de lazos para el sector homogéneo, mientras que para las perturbaciones empleamos una representación más estándar, de tipo Fock. No obstante, analizamos también la generalización de este formalismo híbrido para casos es los que la geometría de FLRW se trata con una propuesta de cuantización más general que la correspondiente a la Gravedad Cuántica de Lazos..

Primordial perturbations in the Dapor-Liegener model of hybrid loop quantum cosmology

In this work, we extend the formalism of hybrid loop quantum cosmology for primordial perturbations around a flat, homogeneous, and isotropic universe to the new treatment of Friedmann-Lema\^itre-Robertson-Walker geometries proposed recently by Dapor and Liegener, based on an alternative regularization of the Hamiltonian constraint. In fact, our discussion is applicable also to other possible regularization schemes for loop quantum cosmology, although we specialize our analysis to the Dapor-Liegener proposal and construct explicitly all involved quantum operators for that case.Comment: 17 page

Unitary evolution and uniqueness of the Fock quantization in flat cosmologies with compact spatial sections

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.Comment: 23 pages. New section 4.2. Added references. Published in EJT

Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes

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.Comment: 15 pages, version accepted for publication in JCA

Cosmological perturbations in Hybrid Loop Quantum Cosmology: Mukhanov-Sasaki variables

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

Gauge invariant formalism for perturbations in quantum cosmology

Presentación de 19 diapositivas; Monash University, Melbourne, Australia, 2-4 December 2015; http://www.asgrg.org/acgrg8/programme/index.htmlPeer Reviewe

Gauge Invariant Perturbations in Quantum Cosmology

Presentación de 21 diapositivas; Quy Nhon, Vietnam, August 9th – 15th, 2015Peer Reviewe

Gauge Invariant Perturbations in Quantum Cosmology

Presentación de 21 diapositivas; Quy Nhon, Vietnam, August 9th – 15th, 2015Peer Reviewe

Mukhanov-Sasaki Equations in Loop Quantum Cosmology

Presentación de 17 diapositivas; Tux, Austria, February 16 to 20, 2015; https://www.gravity.physik.fau.de/events/tux3/tux3.shtmlPeer Reviewe