  The Planck CMB experiment has delivered the best constraints so far on
primordial non-Gaussianity, ruling out early-Universe models of inflation that
generate large non-Gaussianity. Although small improvements in the CMB
constraints are expected, the next frontier of precision will come from future
large-scale surveys of the galaxy distribution. The advantage of such surveys
is that they can measure many more modes than the CMB -- in particular,
forthcoming radio surveys with the SKA will cover huge volumes. Radio continuum
surveys deliver the largest volumes, but with the disadvantage of no redshift
information. In order to mitigate this, we use two additional observables.
First, the integrated Sachs-Wolfe effect -- the cross-correlation of the radio
number counts with the CMB temperature anisotropies -- helps to reduce
systematics on the large scales that are sensitive to non-Gaussianity. Second,
optical data allows for cross-identification in order to gain some redshift
information. We show that, while the single redshift bin case can provide a
sigma(fNL) ~ 20, and is therefore not competitive with current and future
constraints on non-Gaussianity, a tomographic analysis could improve the
constraints by an order of magnitude, even with only two redshift bins. A huge
improvement is provided by the addition of high-redshift sources, so having
cross-ID for high-z galaxies and an even higher-z radio tail is key to enabling
very precise measurements of fNL. Our results show that SKA continuum surveys
could provide constraints competitive with CMB and forthcoming optical surveys,
potentially allowing a measurement of sigma(fNL) ~ 1 to be made. Moreover,
these measurements would act as a useful check of results obtained with other
probes at other redshift ranges with other methods.
