Extending cosmological tests of General Relativity with the Square
  Kilometre Array
  Tests of general relativity (GR) are still in their infancy on cosmological
scales, but forthcoming experiments promise to greatly improve their precision
over a wide range of distance scales and redshifts. One such experiment, the
Square Kilometre Array (SKA), will carry out several wide and deep surveys of
resolved and unresolved neutral hydrogen (HI) 21cm line-emitting galaxies,
mapping a significant fraction of the sky from $0 \le z \lesssim 6$. I present
forecasts for the ability of a suite of possible SKA HI surveys to detect
deviations from GR by reconstructing the cosmic expansion and growth history.
SKA Phase 1 intensity mapping surveys can achieve sub-1\% measurements of
$f\sigma_8$ out to $z\approx 1$, with an SKA1-MID Band 2 survey out to $z
\lesssim 0.6$ able to surpass contemporary spectroscopic galaxy surveys such as
DESI and Euclid in terms of constraints on modified gravity parameters if
challenges such as foreground contamination can be tackled effectively. A more
futuristic Phase 2 HI survey of $\sim10^9$ spectroscopic galaxy redshifts would
be capable of detecting a $\sim 2\%$ modification of the Poisson equation out
to $z\approx 2$.
