Testing foundations of modern cosmology with SKA all-sky surveys

Continuum and HI surveys with the Square Kilometre Array (SKA) will allow us to probe some of the most fundamental assumptions of modern cosmology, including the Cosmological Principle. SKA all-sky surveys will map an enormous slice of space-time and reveal cosmology at superhorizon scales and redshifts of order unity. We illustrate the potential of these surveys and discuss the prospects to measure the cosmic radio dipole at high fidelity. We outline several potentially transformational tests of cosmology to be carried out by means of SKA all-sky surveys.