Galaxy-CMB and galaxy-galaxy lensing on large scales: sensitivity to
  primordial non-Gaussianity
  A convincing detection of primordial non-Gaussianity in the local form of the
bispectrum, whose amplitude is given by the fNL parameter, offers a powerful
test of inflation. In this paper we calculate the modification of two-point
cross-correlation statistics of weak lensing - galaxy-galaxy lensing and
galaxy-Cosmic Microwave Background (CMB) cross-correlation - due to fNL. We
derive and calculate the covariance matrix of galaxy-galaxy lensing including
cosmic variance terms. We focus on large scales (l<100) for which the shape
noise of the shear measurement becomes irrelevant and cosmic variance dominates
the error budget. For a modest degree of non-Gaussianity, fNL=+/-50,
modifications of the galaxy-galaxy lensing signal at the 10% level are seen on
scales R~300 Mpc, and grow rapidly toward larger scales as \propto R^2. We also
see a clear signature of the baryonic acoustic oscillation feature in the
matter power spectrum at ~150 Mpc, which can be measured by next-generation
lensing experiments. In addition we can probe the local-form primordial
non-Gaussianity in the galaxy-CMB lensing signal by correlating the lensing
potential reconstructed from CMB with high-z galaxies. For example, for
fNL=+/-50, we find that the galaxy-CMB lensing cross power spectrum is modified
by ~10% at l~40, and by a factor of two at l~10, for a population of galaxies
at z=2 with a bias of 2. The effect is greater for more highly biased
populations at larger z; thus, high-z galaxy surveys cross-correlated with CMB
offer a yet another probe of primordial non-Gaussianity.
