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The gauge invariant cosmological Jacobi map from weak lensing at leading order
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 convergencedoi:10.48550/arxiv.2201.11552 fatcat:v5ziiijd2bddpdhodiiugpazdi