Publication: Perturbaciones primordiales en Cosmología Cuántica de Lazos
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2017-07-28
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Universidad Complutense de Madrid
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Abstract
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...
The fact that our Universe seems approximately homogeneous and isotropic leads us to expect that its inhomogeneities can indeed be treated as perturbations around a Friedmann- Lemaître-Robertson-Walker (FLRW) background. Actually, the theory of cosmological perturbations, combined with inflation, has proven to give us a good approximation to the anisotropies of the Cosmic Microwave Background, and is able to explain quite satisfactorily the formation of structures at large scales. The principal aim of this thesis is to provide a consistent framework for the quantum description of the evolution of cosmological scalar perturbations (and, by extension, also of tensor perturbations) in the Early Universe. Additionally, this framework is to be designed as to allow us to extract predictions, in the hope that theoretical quantum cosmology models can be eventually falsified with observations, in the current era of "precision cosmology"when this Physics discipline is experiencing a golden age thanks to the recent technical developments that are supplying us with increasingly accurate data. In order to investigate whether it is possible to find information about the genuine quantum nature of the geometry of the spacetime encoded in the imprints left by the quantum fluctuations that occurred in the Early Universe, our quantum description must include, simultaneously, both the background geometry and the cosmological perturbations, with interplay between them. In this thesis, we elaborate a quantization program based on a hybrid approach, which was originally developed for the quantization of inhomogeneous gravitational models in Loop Quantum Cosmology. The strategy consists in splitting the phase space of the considered cosmological system in two: a homogeneous and an inhomogeneous sector. This splitting is attained starting with an expansion in modes of the metric variables and matter fields, using the spatial symmetries. The homogeneous sector incorporates the zeromodes, while the inhomogeneous one includes all the rest of degrees of freedom, present in the perturbations. Then, we proceed to combine different types of quantum representations for each of these parts. More specifically, we use a loop quantization for the homogeneous sector in most of the discussion of this thesis, while a standard Fock representation is applied to the perturbations. Nonetheless, we also analyze the generalization of this hybrid approach, when the FLRW geometry is treated with a more general quantization proposal than just the one arising from Loop Quantum Gravity...
The fact that our Universe seems approximately homogeneous and isotropic leads us to expect that its inhomogeneities can indeed be treated as perturbations around a Friedmann- Lemaître-Robertson-Walker (FLRW) background. Actually, the theory of cosmological perturbations, combined with inflation, has proven to give us a good approximation to the anisotropies of the Cosmic Microwave Background, and is able to explain quite satisfactorily the formation of structures at large scales. The principal aim of this thesis is to provide a consistent framework for the quantum description of the evolution of cosmological scalar perturbations (and, by extension, also of tensor perturbations) in the Early Universe. Additionally, this framework is to be designed as to allow us to extract predictions, in the hope that theoretical quantum cosmology models can be eventually falsified with observations, in the current era of "precision cosmology"when this Physics discipline is experiencing a golden age thanks to the recent technical developments that are supplying us with increasingly accurate data. In order to investigate whether it is possible to find information about the genuine quantum nature of the geometry of the spacetime encoded in the imprints left by the quantum fluctuations that occurred in the Early Universe, our quantum description must include, simultaneously, both the background geometry and the cosmological perturbations, with interplay between them. In this thesis, we elaborate a quantization program based on a hybrid approach, which was originally developed for the quantization of inhomogeneous gravitational models in Loop Quantum Cosmology. The strategy consists in splitting the phase space of the considered cosmological system in two: a homogeneous and an inhomogeneous sector. This splitting is attained starting with an expansion in modes of the metric variables and matter fields, using the spatial symmetries. The homogeneous sector incorporates the zeromodes, while the inhomogeneous one includes all the rest of degrees of freedom, present in the perturbations. Then, we proceed to combine different types of quantum representations for each of these parts. More specifically, we use a loop quantization for the homogeneous sector in most of the discussion of this thesis, while a standard Fock representation is applied to the perturbations. Nonetheless, we also analyze the generalization of this hybrid approach, when the FLRW geometry is treated with a more general quantization proposal than just the one arising from Loop Quantum Gravity...
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Teórica II, leída el 24/06/2016