Weak lensing "post-Born" effects are equivalent to pure lens-lens couplings

TL;DR

This paper demonstrates that weak lensing 'post-Born' effects at 4th order are equivalent to lens-lens couplings within the Born approximation, clarifying the theoretical relationship between these effects and highlighting the need for photon deflection considerations.

Contribution

The paper establishes the equivalence between post-Born effects and lens-lens couplings at 4th order and discusses the necessity of including photon deflection for true post-Born effects.

Findings

Post-Born effects are equivalent to lens-lens couplings at 4th order.

Explicit demonstration of equivalence using anisotropy remapping and Boltzmann approaches.

True post-Born effects require photon deflection terms not included in standard formalisms.

Abstract

We show that the so-called "post-Born" effects of weak lensing at 4th order are equivalent to lens-lens couplings in the Born Approximation. We demonstrate this by explicitly showing the equivalence of the canonical weak lensing approach at 4th order using the anisotropy remapping method, to that of the 4th order calculation of the lens-lens coupling effects using the Boltzmann equation approach that was first developed in [Phys. Rev. D89, 123006]. Furthermore, we argue that to incorporate true "post-Born" effects, i.e. taking into account non-straight photon paths, require the addition of a photon deflection term which has not been taken into account in the canonical formalism nor the Boltzmann method.