The gauge invariant cosmological Jacobi map from weak lensing at leading order

Abstract

We compute the weak lensing Jacobi map at first order in perturbation theory and show that it is both, gauge invariant and symmetric. Linear perturbations therefore do not induce any rotation. However, vector and tensor perturbations do induce B-modes in the shear. We show that contrary to what is often claimed in the literature, the shear B-mode power spectrum is not fully determined by the rotation power spectrum. Also the E-mode shear power spectrum is not determined by the convergence power spectrum. While this difference is small for scalar perturbations, it becomes very relevant for tensor perturbations, i.e. gravitational waves.

A new observable for cosmic shear

“…In [34] the authors do consider rotation but not the rotation induced by shear which is considered in the present paper, rather they consider the rotation from an antisymmetric contribution to the Jacobi map which is much smaller than shear as it appears only at second order in the perturbations [35].…”

“…An additional rotation is in principle also generated by the anti-symmetric part of the Jacobi matrix. But this part is non-vanishing only at second order in perturbation theory [35] and we neglect it here.…”

A new observable for cosmic shear

“…An additional rotation is in principle also generated by the anti-symmetric part of the Jacobi matrix. But this part in non-vanishing only at second order in perturbation theory [18] and we neglect it here.…”