نبذة مختصرة : Our understanding of the Universe has advanced tremendously in the past few decades, with General Relativity(GR) laying the ground for a successful model for the Universe, ΛCDM. However, there are still some fundamental open questions that need to be explored. It is therefore the objective of this thesis to highlight some of these questions by exploring them theoretically and observationally. In the first part of the thesis, the Introduction, I present a background review of GR and ΛCDM. The second part is on testing an essential assumption in Cosmology, the Copernican Principle. By distinguishing between line-of-sight and transverse expansion rates in the most general spacetime possible, one can constrain deviations from the Copernican Principle. Observationally, this is done by measuring polarization of Cosmic Microwave Background(CMB) photons that have been inverse-Compton scattered by galaxy clusters. In the third part, the possibility that Dark Matter(DM) is part of Grav- ity is investigated. On Cosmological scales, this hypothesis is tested with a case study model: Mimetic Dark Matter(MDM). By rederiving the model’s equations of motion, extra free functions and parameters appear in need of fine tuning to produce the observationally certified adiabatic initial conditions. To visualize this, I modify the Boltzmann code CLASS to include MDM, and then look at CMB correlation functions and matter power spectra, which show that deviations of at least 10% from adiabatic initial conditions fall beyond cosmic variance limits. On an astrophysical scale, the hypothesis that DM is part of a modified gravity theory(MGT) is tested by examining DM-devoid galaxies. The main argument is that if DM is part of a MGT, then this phenomenon should be found in every gravitational system. The fact that DM-devoid galaxies exist, while other similar ones are DM dominated, constrains severely the above mentioned hypothesis. To quantify this, I derive a generalized Virial theorem for some MGTs, and show that the extra term gives inconsistent results for DM-devoid galaxies. Therefore, unless fine-tuning is used, DM is more likely to be a non-baryonic particle, or a compact object such as primordial black holes, rather than part of a MGT. The fourth part explores the realm of Quantum Field Theory(QFT) in a gravitational background. The goal is to use neutrinos(spinors) as probes for Dark Energy(DE), to distinguish between its different models. After laying down a general formalism, I first investigate three types of interactions between the two fields, in a semi-classical way, and study the consequences on oscillations of neutrinos and their dynamics. This framework is later generalized to a broader class of interactions between neutrinos, as quantum spinors, and DE, either in the form of a Cosmological Constant(CC) or a scalar field. The result is that different DE models have distinct signatures on neutrino oscillation’s probability. This provides a proof of concept for using neutrino oscillations in curved spacetime as a tool to distinguish between models of the late acceleration of the Universe. To put the above in an observational context, I conclude the fourth part by considering the full three-flavor neutrino oscillations within the ΛCDM paradigm. This results in ternary diagrams and flux plots that could be later compared to observations in neutrino observatories. The conclusion is that one can use neutrino oscillations in curved spacetime to distinguish between different values of the present expansion rate of the Universe, H0. This result adds new insight on the Hubble tension and explores Multimessenger astronomy in its full capacity. The fifth and final part summarizes the results and conclusions reached for each work. In addition, future perspectives and further developments are discussed in this section.
نبذة مختصرة : Nuestra comprensión del Universo ha avanzado enormemente en las últimas décadas, con la Relatividad General(GR) sentando las bases para un modelo exitoso para el Universo, ΛCDM. Sin embargo, todavía quedan algunas cuestiones abiertas fundamentales que deben explorarse. Por tanto, el objetivo de esta tesis es resaltar algunas de estas cuestiones explorándolas teóricamente y observacionalmente. En la primera parte de la tesis, la Introducción, presento una revisión de antecedentes de GR y ΛCDM. La segunda parte trata de probar el principio copernicano. Al distinguir entre las proporciones de expansión en línea- de-visión y transversal en el espacio-tiempo más general posible, se pueden restringir las desviaciones del principio copernicano. Observacionalmente, esto se hace midiendo la polarización de los fotones de fondo cósmico de microondas(CMB) que han sido dispersados en Compton inverso por cúmulos de galaxias. En la tercera parte, investigo la posibilidad que la Materia Oscura(DM) sea parte de las teorías modificadas de gravedad(MGT), tanto a escalas cosmológicas como astrofísicas. En el primero, al investigar un modelo específico, Mimetic Dark Matter(MDM), e incorporarlo en el código de Boltzmann CLASS, muestro que las desviaciones de al menos un 10% de las condiciones iniciales adiabáticas ponen al modelo más allá de la varianza cósmica límites. En escalas astrofísicas, obtengo un teorema de Virial generalizado para algunas MGT, y demuestro que los términos adicionales dan resultados inconsistentes cuando se comparan con galaxias desprovistas de DM. Por lo tanto, a menos que se utilice un ajuste fino, es menos probable que DM forme parte de un MGT. La cuarta parte muestra cómo los neutrinos, cuando se consideran campos de espino cuántico en el espacio-tiempo curvo, podrían distinguir entre modelos de energía oscura. Además, también muestro cómo se puede utilizar esta técnica en la expansión actual del universo, H0 . Este resultado agrega una nueva perspectiva sobre la tensión del Hubble y explora Astronomía de múltiples pasajeros en toda su capacidad. La quinta y última parte resume los resultados y conclusiones alcanzados para cada trabajo. Además, en esta sección se analizan las perspectivas futuras y los desarrollos futuros.
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