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

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 trajectories. 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 in the geodesic equation 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.