Weak lensing B-modes on all scales as a probe of local isotropy

TL;DR

This paper develops a multipolar framework to understand weak-lensing B-modes across all scales, linking their origin to local isotropy and illustrating implications with Bianchi I models.

Contribution

It introduces a general formalism for weak-lensing B-modes in arbitrary spacetimes, extending previous results limited to Friedmann-Lemaître backgrounds.

Findings

B-modes on large scales are connected to local isotropy.

The formalism recovers known results in standard cosmology.

Implications for future observations of anisotropic universes.

Abstract

This article derives a multipolar hierarchy for the propagation of the weak-lensing shear and convergence in a general spacetime. The origin of B-modes, in particular on large angular scales, is related to the local isotropy of space. Known results assuming a Friedmann-Lema\^itre background are naturally recovered. The example of a Bianchi I spacetime illustrates our formalism and its implications for future observations are stressed.