On the validity of the Born approximation for beyond-Gaussian weak lensing observables

TL;DR

This study evaluates the accuracy of the Born approximation in weak lensing simulations, finding it sufficiently precise for power spectrum analysis but introducing biases in higher-order statistics, with significant computational savings.

Contribution

The paper demonstrates that the Born approximation accurately reproduces certain weak lensing observables and quantifies its limitations for higher-order statistics, supported by simulations.

Findings

Born approximation deviations align with O(Φ^3) corrections.

Negligible bias in power spectrum for LSST-like surveys.

Significant bias up to 2.5σ in skewness and kurtosis.

Abstract

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the non-linear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray-tracing through the outputs of $N$-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray--traced counterparts are consistent with the smallest non-trivial $O(\Phi^3)$ post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger $O(\Phi^4)$ (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born approximated power spectrum is negligible even for an LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the $\kappa$ skewness and kurtosis, however, we find significant bias of up to 2.5$\sigma$. Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray-tracing in reconstructing the convergence.