Probing Cosmology beyond $\Lambda$CDM using the SKA

The cosmological principle states that the Universe is statistically homogeneous and isotropic at large distance scales. There currently exist many observations which indicate a departure from this principle. It has been shown that many of these observations can be explained by invoking superhorizon cosmological perturbations and may be consistent with the Big Bang paradigm. Remarkably, these modes simultaneously explain the observed Hubble tension, i.e., the discrepancy between the direct and indirect measurements of the Hubble parameter. We propose several tests of the cosmological principle using SKA. In particular, we can reliably extract the signal of dipole anisotropy in the distribution of radio galaxies. The superhorizon perturbations also predict a significant redshift dependence of the dipole signal which can be nicely tested by the study of signals of reionization and the dark ages using SKA. We also propose to study the alignment of radio galaxy axes as well as their integrated polarization vectors over distance scales ranging from a few Mpc to Gpc. We discuss data analysis techniques that can reliably extract these signals from data.