Are we living near the center of a local void?

TL;DR

This paper investigates how a local void affects CMB anisotropies, revealing unique off-diagonal correlations that could distinguish geometric effects from kinematic ones in observations.

Contribution

It provides a detailed analysis of CMB anisotropies for an off-centered observer in a local void, including off-diagonal correlators and their implications.

Findings

Off-diagonal correlators are non-zero due to the local void.

Lensing-like effects persist even after velocity adjustments.

Signature differences can help distinguish geometric from kinematic effects.

Abstract

The properties of the cosmic microwave background (CMB) temperature and polarisation anisotropies measured by a static, off-centered observer located in a local spherically symmetric void, are described. In particular in this paper we compute, together with the standard 2- point angular correlation functions, the off-diagonal correlators, which are no more vanishing by symmetry. While the energy shift induced by the off-centered position of the observer can be suppressed by a proper choice of the observer velocity, a lensing-like effect on the CMB emission point remains. This latter effect is genuinely geometrical (e.g. non-degenerate with a boost) and reflects in the structure of the off-diagonal correlators. At lowest order in this effect, the temperature and polarisation correlation matrices have non-vanishing diagonal elements, as usual, and all the off-diagonal terms are excited. This particular signature of a local void model allows one, in principle, to disentangle geometrical effects from local kinematical ones in CMB observations.