Second Order Geodesic Corrections to Cosmic Shear

We consider the impact of second order corrections to the geodesic equation governing gravitational lensing. We start from the full second order metric, including scalar, vector, and tensor perturbations, and retain all relevant contributions to the cosmic shear corrections that are second order in the gravitational potential. The relevant terms are: the nonlinear evolution of the scalar gravitational potential, the Born correction, and lens-lens coupling. No other second order terms contribute appreciably to the lensing signal. Since ray-tracing algorithms currently include these three effects, this derivation serves as rigorous justification for the numerical predictions.