About the foundations of modern cosmology: cosmological tests of the Copernican principle.

The standard paradigm of modern cosmology relies on a set of fundamental assumptions that simplify and make possible the modeling of the Universe. Among these critical hypotheses, there is the presumption that we do not occupy a special place in the Universe, the so-called Copernican principle. The assumption of this principle constrains the degrees of freedom allowed by the theory, and, in particular, leads to a spatially homogeneous and isotropic space-time. We present a program to observationally test the Copernican principle. Using the latest cosmological data, we test the Copernican principle by placing constraints on radial deviations of the FLRW space-time. We also forecast the precision with which future surveys, such as DES, Euclid, and LSST, will be able to test the Copernican principle and test their ability to detect any possible violations. Furthermore, we investigate if the 5σ discrepancy between the early and late times determinations of the Hubble constant could be a hint of a violation of the assumption of homogeneity.