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) crosscorrelation-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∼300Mpc, and grow rapidly toward larger scales as ∝R2. We also see a clear signature of the baryonic acoustic oscillation feature in the matter power spectrum at ∼150Mpc, 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 2 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.