Full-sky lensing shear at second order

Understand

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.