Lorentz and diffeomorphism violation in efective theories of gravity and matter.
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Date
2025
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Universidad de Concepción
Abstract
En la presente tesis se estudió en profundidad el sector minimal de la extensión del Modelo Estándar Gravitacional (gSME) en un escenario cosmológico, con el objetivo de desvelar las condiciones de compatibilidad entre los campos background y la dinámica de la teoría. Para ello, se analizó el rompimiento explícito y espontáneo de la invariancia bajo difeomorfismos de la Relatividad General dentro del marco de las teorías efectivas. En ambos casos se derivaron las ecuaciones de Friedmann modificadas, así como las configuraciones requeridas por los campos de background para preservar la isotropía y la homogeneidad. En este contexto, se identificaron configuraciones que permiten multiples fases de expansión del universo.
Este estudio condujo al desarrollo de un método para tratar las incompatibilidades entre las violaciones explícitas de difeomorfismos y la geometría Riemanniana, basado en el análisis de las isometrías de un sistema gravitacional. Se concluye que las configuraciones de los campos de background son más propensas a determinarse cuanto mayor sea el número de difeomorfismos que actúan como isometrías del sistema en el caso de rompimiento explícito; en cambio, en el caso de rompimiento espontáneo, el campo de background no requiere respetar dichas isometrías para garantizar la compatibilidad. Prueba de la efectividad del método, se logra estudiar violaciones de causalidad en presencia de campos de background de forma consistente.
This thesis conducted an in-depth study of the minimal sector of the gravitational Standard-Model Extension (gSME) in a cosmological scenario, with the aim of uncovering the compatibility conditions between the background fields and the dynamics of the theory. To this end, the explicit and spontaneous breaking of diffeomorphism invariance in General Relativity was analyzed within the framework of effective field theories. In both cases, the modified Friedmann equations were derived, as well as the configurations required by the background fields to preserve isotropy and homogeneity. In this context, configurations that allow for multiple phases of universe expansion were identified. This study led to the development of a method for addressing the incompatibilities between explicit diffeomorphism violations and Riemannian geometry, based on the analysis of the isometries of a gravitational system. It is concluded that the configurations of the background fields are more likely to be determined the greater the number of diffeomorphisms that act as isometries of the system in the case of explicit breaking; in contrast, in the case of spontaneous breaking, the background f ield does not need to respect these isometries to guarantee compatibility. As proof of the method’s effectiveness, causality violations in the presence of background f ields were consistently studied.
This thesis conducted an in-depth study of the minimal sector of the gravitational Standard-Model Extension (gSME) in a cosmological scenario, with the aim of uncovering the compatibility conditions between the background fields and the dynamics of the theory. To this end, the explicit and spontaneous breaking of diffeomorphism invariance in General Relativity was analyzed within the framework of effective field theories. In both cases, the modified Friedmann equations were derived, as well as the configurations required by the background fields to preserve isotropy and homogeneity. In this context, configurations that allow for multiple phases of universe expansion were identified. This study led to the development of a method for addressing the incompatibilities between explicit diffeomorphism violations and Riemannian geometry, based on the analysis of the isometries of a gravitational system. It is concluded that the configurations of the background fields are more likely to be determined the greater the number of diffeomorphisms that act as isometries of the system in the case of explicit breaking; in contrast, in the case of spontaneous breaking, the background f ield does not need to respect these isometries to guarantee compatibility. As proof of the method’s effectiveness, causality violations in the presence of background f ields were consistently studied.
Description
Tesis presentada para optar al grado de Doctor en Ciencias Físicas.
Keywords
Diffeomorphisms, Broken symmetry (Physics), Gravity, Geometry Riemannian