Weak-lensing by the large scale structure in a spatially anisotropic universe: theory and predictions

TL;DR

This paper develops a theoretical framework for analyzing weak gravitational lensing in an anisotropic universe, predicting observable signatures such as B-modes and off-diagonal correlations that can test cosmic isotropy.

Contribution

It introduces a novel analytical approach to compute weak-lensing correlators in an anisotropic universe, linking observable spectra to late-time anisotropy and expansion eigendirections.

Findings

B-modes serve as tracers of late-time anisotropy.

Off-diagonal correlations reveal eigendirections of expansion.

Predictions are applicable to future surveys like Euclid and SKA.

Abstract

This article details the computation of the two-point correlators of the convergence, $E$- and $B$-modes of the cosmic shear induced by the weak-lensing by large scale structure assuming that the background spacetime is spatially homogeneous and anisotropic. After detailing the perturbation equations and the general theory of weak-lensing in an anisotropic universe, it develops a weak shear approximation scheme in which one can compute analytically the evolution of the Jacobi matrix. It allows one to compute the angular power spectrum of the $E$- and $B$-modes. In the linear regime, the existence of $B$-modes is a direct tracer of a late time anisotropy and their angular power spectrum scales as the square of the shear. It is then demonstrated that there must also exist off-diagonal correlations between the $E$-modes, $B$-modes and convergence that are linear in the geometrical shear and allow one to reconstruct the eigendirections of expansion. These spectra can be measured in future large scale surveys, such as Euclid and SKA, and offer a new tool to test the isotropy of the expansion of the universe at low redshift.