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Weak Lensing of the CMB: Cumulants of the Probability Distribution Function

Michael Kesden·Asantha Cooray·Marc Kamionkowski
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Abstract

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, non-zero 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.

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Michael Kesden, Asantha Cooray, Marc Kamionkowski. 2002-08-16. Weak Lensing of the CMB: Cumulants of the Probability Distribution Function. https://doi.org/10.1103/physrevd.66.083007

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