The Born and lens-lens corrections to weak gravitational lensing angular power spectra

We revisit the estimation of higher order corrections to the angular power spectra of weak gravitational lensing. Extending a previous calculation of Cooray and Hu, we find two additional terms to the fourth order in potential perturbations of large-scale structure corresponding to corrections associated with the Born approximation and the neglect of line-of-sight coupling of two foreground lenses in the standard first order result. These terms alter the convergence (kappa kappa), the lensing shear E-mode (epsilon epsilon), and their cross-correlation (kappa epsilon) power spectra on large angular scales, but leave the power spectra of the lensing shear B-mode (beta beta) and rotational (ww) component unchanged as compared to previous estimates. The new terms complete the calculation of corrections to weak lensing angular power spectra associated with both the Born approximation and the lens-lens coupling to an order in which the contributions are most significant. Taking these features together, we find that these corrections are unimportant for any weak lensing survey, including for a full sky survey limited by cosmic variance.