The Gravitational Lensing Effect on the CMB Polarisation Anisotropy in the {\Lambda}-LTB Model

TL;DR

This paper investigates how a local void affects CMB polarisation via gravitational lensing, producing observable B-modes from E-modes, and proposes a method to distinguish this effect from galaxy shear.

Contribution

The authors derive formulas for CMB polarisation correlations in the LTB model, highlighting unique signatures of local void lensing on E and B modes.

Findings

E-B mode correlations are proportional to δ_{l,l'}

E-E correlations are proportional to δ_{|l'-l|, 1}

Distinctive signatures can differentiate local void lensing from galaxy shear

Abstract

A local void modifies the sky distribution pattern of the cosmic microwave background (CMB) polarisation by gravitational lensing and produces B-modes from E-modes for an off-center observer. In order to see whether this effect can be used to observationally test the validity of the local void model, we calculate this lensing effect by solving the propagation of CMB polarisation along null geodesics close to the central light cone in the general Lema\^itre-Tolman-Bondi (LTB) model perturbatively. In particular, we give general formulas for the correlations of E and B observed by an off-center observer and show that E_l^m and B_l^m are correlated for the same value of l, i.e., <E_l^m B_l'^m'> is proportional to {\delta}_{l, l'}, while <E_l^m E_l'^m'> is proportional to {\delta}_{|l'-l|, 1}. This feature can be used to distinguish the gravitational lensing effect by a local void from those by normal shear field of galaxies.