Non-Gaussian signature of weak gravitational lensing in the CMB

Inflationary cosmologies predict Gaussian primordial fluctuations, but subsequent gravitational lensing of the CMB disturbs its Gaussianity. Knowledge of the specific signature of lensing is necessary to distinguish a lensed Gaussian sky from an intrinsically non-Gaussian one. In this paper we investigate the pattern of non-Gaussian features in the CMB resulting from gravitational lensing, both analytically and numerically. We describe the lensed CMB temperature distribution using the formalism of generating functionals and obtain the complete picture of emerging non-Gaussian effects. To test for the signature of lensing in practice, we propose a scale-dependent statistic based on cumulants of the CMB temperature, and we compute that statistic numerically for typical inflationary models. The effect is expected to be most significant at angular scales $\sim 10^\prime$ and its magnitude is within observational capabilities of future satellite missions.