# Accurately computing weak lensing convergence

## TL;DR

This paper quantifies the necessary relativistic corrections, including post-Born and lens-lens coupling effects, to achieve sub-percent accuracy in weak lensing convergence predictions up to redshift 2, crucial for upcoming cosmological surveys.

## Contribution

It provides the first relativistic quantification of how many higher-order corrections are needed for accurate weak lensing convergence modeling in cosmology.

## Key findings

- Including lens-lens coupling and post-Born corrections up to second and third order achieves sub-percent accuracy for 94% of light rays.
- A significant portion of rays exhibit post-Born corrections exceeding 10% of the gravitational convergence.
- Some rays at redshift 2 have post-Born corrections several times larger than the first-order convergence.

## Abstract

Weak lensing will play an important role in future cosmological surveys, including e.g. Euclid and SKA. Sufficiently accurate theoretical predictions are important for correctly interpreting these surveys and hence for extracting correct cosmological parameter estimations. We quantify for the first time in a relativistic setting how many post-Born and lens-lens coupling corrections are required for sub-percent accuracy of the theoretical weak lensing convergence for $z\le 2$ (the primary weak lensing range for Euclid and SKA). We do this by ray-tracing through a fully relativistic exact solution of the Einstein Field Equations which consists of randomly packed mass-compensated underdensities of realistic amplitudes. We find that including lens-lens coupling terms and post-Born corrections up to second and third order respectively is sufficient for sub-percent accuracy of the convergence along $94\%$ of the studied light rays. We also find that a significant percentage of the studied rays have post-Born corrections of size over $10\%$ of the usual gravitational convergence, $\kappa^{(1)}$, and several rays even have post-Born corrections several times the size of $\kappa^{(1)}$ at $z = 2$.