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Second Order Corrections to Weak Lensing by Large-Scale Structure

We calculate corrections to the power spectrum predictions of weak lensing by large scale structure due to higher order effects in the gravitational potential. Using a perturbative approach to third order in transverse displacements, we calculate a second order correction to the angular power spectra of E and B mode shear and convergence resulting from dropping the so-called Born approximation, where one integrates along the unperturbed photon path. We also consider a correction to the power spectra from the coupling between lenses at different redshifts. Both effects generate B-mode shear and the latter also causes a net rotation of the background galaxy images. We show all these corrections are at least two orders of magnitude below the convergence or E-mode power and hence relevant only to future ultra high precision measurements. These analytical calculations are consistent with previous numerical estimates and validate the use of current large scale structure weak lensing predictions for cosmological studies and future use of B-modes as a monitor of systematic effects.