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 HI galaxies, eventually covering 30,000 sq. deg. and
reaching out to redshift z~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 fNL can be constrained down to an
accuracy of 1.54. This improves the current limit set by the Planck satellite
by a factor of five, using a completely different approach.
