Full-sky lensing shear at second order

TL;DR

This paper derives a comprehensive second-order full-sky model for cosmic shear, including relativistic effects and non-linear couplings, crucial for accurate large-scale weak lensing analyses.

Contribution

It presents the first full-sky second-order calculation of cosmic shear incorporating vector, tensor, and relativistic effects without small-angle approximations.

Findings

Identifies new non-linear couplings in cosmic shear.

Highlights importance of relativistic effects on large angular scales.

Provides a framework for higher-order weak lensing observables.

Abstract

We compute the reduced cosmic shear up to second order in the gravitational potential without relying on the small angle or thin-lens approximation. This is obtained by solving the Sachs equation which describes the deformation of the infinitesimal cross-section of light bundle in the optical limit, and maps galaxy intrinsic shapes into their angular images. The calculation is done in the Poisson gauge without a specific matter content, including vector and tensor perturbations generated at second order and taking account of the inhomogeneities of a fixed redshift source plane. Our final result is expressed in terms of spin-2 operators on the sphere and is valid on the full sky. Beside the well known lens-lens and Born corrections that dominate on small angular scales, we find new non-linear couplings. These are a purely general relativistic intrinsic contribution, a coupling between the gravitational potential at the source with the lens, couplings between the time delay with the lens, couplings between two photon deflections, as well as non-linear couplings due to the second-order vector and tensor components. The inhomogeneity in the redshift of the source induces a coupling between the photon redshift with the lens. All these corrections become important on large angular scales and should thus be included when computing higher-order observables such as the bispectrum, in full or partially full-sky surveys.