Observational Tests of the Cosmological Paradigm and the Phenomenology of its Extensions.

As we usher in the era of precision cosmology, the inconsistencies that afflict the cosmological paradigm, also known as the “ΛCDM model”, prompt us to question its validity as a description of the universe and challenge its foundations. This Thesis explores different ways of tackling three present and persistent issues: the lensing anomaly, the Hubble tension and the value of the spatial curvature of the universe. This is done, respectively, by introducing extensions from the standard picture in the form of modifications of gravity, dark energy and deviations from spatial flatness. After introducing the basic tools needed to understand the theoretical underpinnings of the ΛCDM model, along with the observational and statistical methods required to test its robustness against the state-of-the-art cosmological datasets, five chapters present a series of five papers that make up the bulk of this Thesis. The results of these works are, in order, a proof that the lensing anomaly can be recast in terms of modified gravity, an alleviation of the Hubble tension and an improvement in the currently available constraints of the spatial curvature. In retrospect, these results offer new and original takes on the limits of our standard model of the universe, which the upcoming cosmological surveys are set to constrain more precisely than ever before.