Access provided through the subscription of CEA SACLAY

Phys. Rev. D 81, 083002 (2010) [15 pages]

Full-sky lensing shear at second order

Download: PDF (237 kB) Export: BibTeX or EndNote (RIS)

Francis Bernardeau, Camille Bonvin, and Filippo Vernizzi
CEA, Institut de Physique Théorique, 91191 Gif-sur-Yvette cédex, France, CNRS, URA-2306, 91191 Gif-sur-Yvette cédex, France

Received 25 November 2009; published 5 April 2010

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 a 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 nonlinear 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 and between two photon deflections, as well as nonlinear 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.

© 2010 The American Physical Society

95.30.Sf, 98.65.Dx, 98.80.Es, 98.80.Jk