Weak lensing in non-statistically isotropic universes

TL;DR

This paper develops a formalism using Bipolar Spherical Harmonics to analyze weak lensing effects on the CMB in universes that are not statistically isotropic, extending standard models to more general cosmological scenarios.

Contribution

It introduces a BipoSH-based framework for describing CMB weak lensing in non-statistically isotropic universes, generalizing existing isotropic models.

Findings

BipoSH coefficients encode complete statistical information of non-SI Gaussian CMB.

The formalism reduces to standard weak lensing results in the isotropic limit.

Provides a new tool for analyzing anisotropic features in CMB data.

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.