Constraining primordial non-Gaussianity using two galaxy surveys and CMB
  lensing
  Next-generation galaxy surveys will be able to measure perturbations on
scales beyond the equality scale. On these ultra-large scales, primordial
non-Gaussianity leaves signatures that can shed light on the mechanism by which
perturbations in the early Universe are generated. We perform a forecast
analysis for constraining local type non-Gaussianity and its two-parameter
extension with a simple scale-dependence. We combine different clustering
measurements from future galaxy surveys -- a 21cm intensity mapping survey and
two photometric galaxy surveys -- via the multi-tracer approach. Furthermore we
then include CMB lensing from a CMB Stage 4 experiment in the multi-tracer,
which can improve the constraints on bias parameters. We forecast
$\sigma(f_{\rm NL}) \simeq 0.9$ (1.4) by combining SKA1, a Euclid-like
(LSST-like) survey, and CMB-S4 lensing. With CMB lensing, the precision on
$f_{\rm NL}$ improves by up to a factor of 2, showing that a joint analysis is
important. In the case with running of $f_{\rm NL}$, our results show that the
combination of upcoming cosmological surveys could achieve $\sigma(n_{\rm NL})
\simeq 0.12$ (0.22) on the running index.
