Resumen:
This work aims to conduct a consistency test of the Cosmological Principle, one of the fundamental hypotheses of the Standard Cosmological Model. This principle postulates that the Universe is homogeneous and isotropic on large scales. By testing it, we end up reviewing the foundations of the Standard Cosmological Model. Through a consistency relationship between measurements of ages and cosmological distances, we verify, in this work, whether there is evolution in the redshift of the curvature parameter, . If we find that is not constant, we have evidence of a deviation from the homogeneity hypothesis and, consequently, there is no consistency with the Cosmological Principle. We use a compilation of distance measurements from type Ia Supernovae from the Pantheon+SH0ES collaboration and a compilation of Hubble parameter measurements, Hpzq, obtained by galaxy ages and baryon acoustic oscillations, to calculate Ωk. Through non-parametric reconstructions via Gaussian Processes, we show that there is no significant evolution of the curvature parameter, , as a function of redshift, and that there is in agreement with the Standard Cosmological Model. However, the uncertainties in our analyses are still quite high. We also show that these uncertainties can be significantly reduced through simulations of redshift survey data, as well as gravitational waves.
