Lensing of the CMB: Non Gaussian aspects

We study the generation of CMB anisotropies by gravitational lensing on small angular scales. We show these fluctuations are not Gaussian. We prove that the power spectrum of the tail of the CMB anisotropies on small angular scales directly gives the power spectrum of the deflection angle. We show that the generated power on small scales is correlated with the large scale gradient. The cross correlation between large scale gradient and small scale power can be used to test the hypothesis that the extra power is indeed generated by lensing. We compute the three and four point function of the temperature in the small angle limit. We relate the non-Gaussian aspects presented in this paper as well as those in our previous studies of the lensing effects on large scales to the three and four point functions. We interpret the statistics proposed in terms of different configurations of the four point function and show how they relate to the statistic that maximizes the S/N.Comment: Changes to match accepted version in PRD, 20 pages 10 figures. Better resolution images of the figures can be found at http://www.sns.ias.edu/~matiasz/RESEARCH/cmblensing.htm