Weak-lensing $B$-modes as a probe of the isotropy of the universe

TL;DR

This paper proposes using weak-lensing B-modes and their correlations with E-modes and convergence as a novel method to detect and measure anisotropy in the universe's expansion, with potential for high-precision constraints.

Contribution

It introduces a new approach to probe cosmic anisotropy through the angular power spectrum of weak-lensing B-modes and off-diagonal correlations, applicable to future surveys.

Findings

Off-diagonal correlations enable reconstruction of expansion eigendirections.

Future surveys can constrain geometrical shear at percent-level accuracy.

Method offers a powerful new probe of cosmological isotropy.

Abstract

We compute the angular power spectrum of the $B$-modes of the weak-lensing shear in a spatially anisotropic spacetime. We find that there must also exist off-diagonal correlations between the $E$-modes, $B$-modes, and convergence that allow one to reconstruct the eigendirections of expansion. Focusing on future surveys such as Euclid and SKA, we show that observations can constrain the geometrical shear in units of the Hubble rate at the percent level, or even better, offering a new and powerful method to probe our cosmological model.