The Gravitational Lensing Effect on the CMB Polarisation Anisotropy in the Λ-LTB Model

• Published in: Progress of theoretical and experimental physics 2011-04, Vol.125 (4), p.815-836
• Main Authors: Goto, Hajime, Kodama, Hideo
• Format: Article
• Language: English
• ISSN: 0033-068X; 2050-3911; 1347-4081
• DOI: 10.1143/PTP.125.815

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 Lemaître-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 m ℓ and B m ℓ are correlated for the same value of ℓ, i.e., 〈E m ℓ B m′ ℓ′〉 ∝ δℓ,′ℓ, while 〈E m ℓ E m′ ℓ′〉 ∝ δ|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.