Probing cosmic isotropy: Hubble constant and matter density large-angle variations with the Pantheon+SH0ES data

In this study we investigate potential large-angle anisotropies in the angular distribution of the cosmological parameters $H_0$ (the Hubble constant) and $\Omega_m$ (the matter density) in the flat-$\Lambda$CDM framework, using the Pantheon+SH0ES supernovae catalog. For this we perform a directional analysis by dividing the celestial sphere into a set of directions, and estimate the best-fit cosmological parameters across the sky using a MCMC approach. Our results show a dominant dipolar pattern for both parameters in study, suggesting a preferred axis in the universe expansion and in the distribution of matter. However, we also found that for $z \gtrsim 0.015$, this dipolar behavior is not statistically significant, confirming the expectation -- in the $\Lambda$CDM scenario -- of an isotropic expansion and a uniform angular distribution of matter (both results at $1\,\sigma$ confidence level). Nevertheless, for nearby supernovae, at distances $\lesssim 60$ Mpc or $z \lesssim 0.015$, the peculiar velocities introduce a highly significant dipole in the angular distribution of $H_0$. Furthermore, we perform various robustness tests that support our findings, and consistency tests of our methodology.