G. Fanizza, E. Di Dio, R. Durrer, G. Marozzi
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 significant for tensor perturbations, i.e. gravitational waves.
Keywords
Cosmological perturbation theory in GR and beyond; gravitational lensing; gravitational waves / theory; weak gravitational lensing; Astrophysics - Cosmology and Nongalactic Astrophysics; General Relativity and Quantum Cosmology
Journal of Cosmology and Astroparticle Physics
Volume 2022, Issue 8
2022 August
