Probing primordial non-Gaussianity with SKA galaxy redshift surveys: a fully relativistic analysis

The Square Kilometre Array (SKA) will produce spectroscopic surveys of tens to hundreds of millions of neutral hydrogen (H I) galaxies, eventually covering 30 000 deg(2) and reaching out to redshift z greater than or similar to 2. The huge volumes probed by the SKA will allow for some of the best constraints on primordial non-Gaussianity, based on measurements of the large-scale power spectrum. We investigate various observational set-ups for HI galaxy redshift surveys, compatible with the SKA Phase 1 and Phase 2 (full SKA) configurations. We use the corresponding number counts and bias for each survey from realistic simulations and derive the magnification bias and the evolution of source counts directly from these. For the first time, we produce forecasts that fully include the general relativistic effects on the galaxy number counts. These corrections to the standard analysis become important on very large scales, where the signal of primordial non-Gaussianity grows strongest. Our results show that, for the full survey, the non-Gaussianity parameter f(NL) can be constrained down to sigma(f(NL)) = 1.54. This improves the current limit set by the Planck satellite by a factor of 5, using a completely different approach.