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 $f_{\mathrm{NL}}$ 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) crosscorrelation—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 $R\sim 300\mathrm{Mpc}$, 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 $\sim 150\mathrm{Mpc}$, 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 2 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.