Cosmology without the cosmological principle: A study of the large-scale structure effects in the background universe

Abstract: Recent studies strongly suggest that the $Λ$CDM model may no longer serve as the definitive standard model in cosmology, given the increasing tensions between different cosmological observables. Some researchers have described this situation as a "crisis in cosmology." The $Λ$CDM model relies on two fundamental assumptions: the isotropy of the universe (supported by observational evidence) and the Copernican principle (a philosophical postulate). Together, these assumptions lead to the well-known Cosmological Principle, with the homogeneity of the universe emerging as a direct consequence. In this thesis, I review the cosmological consequences of relaxing some of these assumptions, exploring inhomogeneous and anisotropic universe models, as well as tilted cosmologies, which consider observers in motion relative to the Hubble flow. We examine methods to study these effects using existing cosmological data. First, we explore a variety of models that describe inhomogeneous and anisotropic universes, including different metric theories, perturbative analyses, averaging effects, tilted scenarios, and cosmographic approaches. We then apply this theoretical framework to analyze SNIA data and the local peculiar velocity field, aiming to constrain key parameters.