  The study of the Universe on ultra-large scales is one of the major science
cases for the Square Kilometre Array (SKA). The SKA will be able to probe a
vast volume of the cosmos, thus representing a unique instrument, amongst
next-generation cosmological experiments, for scrutinising the Universe's
properties on the largest cosmic scales. Probing cosmic structures on extremely
large scales will have many advantages. For instance, the growth of
perturbations is well understood for those modes, since it falls fully within
the linear regime. Also, such scales are unaffected by the poorly understood
feedback of baryonic physics. On ultra-large cosmic scales, two key effects
become significant: primordial non-Gaussianity and relativistic corrections to
cosmological observables. Moreover, if late-time acceleration is driven not by
dark energy but by modifications to general relativity, then such modifications
should become apparent near and above the horizon scale. As a result, the SKA
is forecast to deliver transformational constraints on non-Gaussianity and to
probe gravity on super-horizon scales for the first time.
