On the validity of the Born approximation for weak cosmic flexions

TL;DR

This paper investigates the accuracy of the Born approximation in weak cosmic flexion lensing, finding it to be generally valid except at very small scales, by analyzing lens-lens couplings and higher-order effects.

Contribution

It provides a perturbative analysis of lens-lens couplings and Born approximation effects on cosmic flexion, introducing a diagrammatic representation and new correction terms.

Findings

Born approximation is accurate for most scales in cosmic flexion

Dropping the Born approximation introduces additional twist components

Corrections become significant only at very small scales

Abstract

Weak lensing calculations are often made under the assumption of the Born approximation, where the ray path is approximated as a straight radial line. In addition, lens-lens couplings where there are several deflections along the light ray are often neglected. We examine the effect of dropping the Born approximation and taking lens-lens couplings into account, for weak lensing effects up to second order (cosmic flexion), by making a perturbative expansion in the light path. We present a diagrammatic representation of the resulting corrections to the lensing effects. The flexion signal, which measures the derivative of the density field, acquires correction terms proportional to the squared gravitational shear; we also find that by dropping the Born approximation, two further degrees of freedom of the lensing distortion can be excited (the twist components), in addition to the four standard flexion components. We derive angular power spectra of the flexion and twist, with and without the Born-approximation and lens-lens couplings and confirm that the Born approximation is an excellent approximation for weak cosmic flexions, except at very small scales.