# CMB weak-lensing beyond the Born approximation: a numerical approach

## TL;DR

This paper investigates the effects of beyond-Born gravitational lensing on CMB anisotropies using advanced numerical simulations, revealing small but significant corrections to lensing observables and polarization rotation, with implications for future experiments.

## Contribution

It introduces a comprehensive numerical approach to quantify beyond-Born lensing effects on the CMB, extending previous analytical predictions to smaller scales and including polarization rotation.

## Key findings

- Good agreement with analytical predictions for lensing corrections.
- Beyond-Born effects are detectable in temperature spectra with foreground control.
- Polarization corrections are challenging to measure with upcoming experiments.

## Abstract

We perform a complete study of the gravitational lensing effect beyond the Born approximation on the Cosmic Microwave Background (CMB) anisotropies using a multiple-lens raytracing technique through cosmological N-body simulations of the DEMNUni suite. The impact of second order effects accounting for the non-linear evolution of large-scale structures is evaluated propagating for the first time the full CMB lensing jacobian together with the light rays trajectory. We carefully investigate the robustness of our approach against several numerical effects in the raytracing procedure and in the N-body simulation itself, and find no evidence of large contaminations. We discuss the impact of beyond-Born corrections on lensed CMB observables, and compare our results with recent analytical predictions that appeared in the literature, finding a good agreement, and extend these results to smaller angular scales. We measure the gravitationally-induced CMB polarization rotation that appears at second order, and compare this result with the latest analytical predictions. We then present the detection prospect of beyond-Born effects with the future CMB-S4 experiment. We show that corrections to the temperature power spectrum can be measured only if a good control of the extragalactic foregrounds is achieved. Conversely, the beyond-Born corrections on E and B-modes power spectra will be much more difficult to detect.