Weak lensing in non-statistically isotropic universes

Abstract

The Bipolar Spherical Harmonics (BipoSH) form a natural basis to study the CMB two point correlation function in a non-statistically isotropic (non-SI) universe. The coefficients of expansion in this basis are a generalisation of the well known CMB angular power spectrum and contain complete information of the statistical properties of a non-SI but Gaussian random CMB sky. We use these coefficients to describe the weak lensing of CMB photons in a non-SI universe. Finally we show that the results reduce to the standard weak lensing results in the isotropic limit.