Numerical study of statistical properties of the lensing excursion angles

We present ray tracing simulations combined with sets of large N-body simulations. Experiments were performed to explore, for the first time, statistical properties of fluctuations in angular separations of nearby light ray pairs (the so-called lensing excursion angle) induced by weak lensing by large-scale structures. We found that the probability distribution function (PDF) of the lensing excursion angles is not simply Gaussian but has an exponential tail. It is, however, found that the tail, or more generally non-Gaussian nature in the PDF has no significant impact on the weak lensing of the CMB. Moreover, we found that the variance in the lensing excursion angles predicted by the power spectrum approach is in good agreement with our numerical results. These results demonstrate a validity of using the power spectrum approach to compute lensing effects on the CMB.