A convincing detection of primordial non-Gaussianity in the local form of the bispectrum , whose amplitude is given by the f _ { \mathrm { NL } } 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 f _ { \mathrm { NL } } .
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 , f _ { \mathrm { NL } } = \pm 50 , modifications of the galaxy-galaxy lensing signal at the 10 % level are seen on scales R \sim 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 \sim 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 f _ { \mathrm { NL } } = \pm 50 , we find that the galaxy-CMB lensing cross power spectrum is modified by \sim 10 % at l \sim 40 , and by a factor of two at l \sim 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 .