Weak lensing of the CMB: Cumulants of the probability distribution function
We discuss the real-space moments of temperature anisotropies in the cosmic microwave background (CMB) due to weak gravitational lensing by intervening large-scale structure. We show that if the probability distribution function of primordial temperature anisotropies is Gaussian, then it remains unchanged after gravitational lensing. With finite resolution, however, nonzero higher-order cumulants are generated both by lensing autocorrelations and by cross-correlations between the lensing potential and secondary anisotropies in the CMB such as the Sunayev-Zel'dovich (SZ) effect. Skewness is produced by these lensing-SZ correlations, while kurtosis receives contributions from both lensing alone and lensing-SZ correlations. We show that if the projected lensing potential is Gaussian, all cumulants of higher order than the kurtosis vanish. While recent results raise the possibility of detection of the skewness in upcoming data, the kurtosis will likely remain undetected.
Additional Information© 2002 The American Physical Society. Received 16 August 2002; published 29 October 2002. This work was supported in part by NSF AST-0096023, NASA NAG5-8506, and DoE DE-FG03-92-ER40701. Kesden acknowledges the support of the NSF Graduate program, and A.C. acknowledges support from the Sherman Fairchild Foundation.
Published - KESprd02.pdf