CMB-lensing beyond the Born approximation

TL;DR

This paper explores corrections to CMB lensing beyond the Born approximation using third-order gravitational potential effects, revealing a new non-Gaussian contribution that is currently too small to detect.

Contribution

It introduces the first calculation of the non-Gaussian deflection angle contribution to CMB lensing beyond the Born approximation, highlighting its significance among post-Born corrections.

Findings

Non-Gaussian deflection angle contribution is the leading post-Born correction.

The effect is smaller than non-linear matter power spectrum corrections.

Current experiments cannot detect this correction.

Abstract

We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles $\ell\lesssim 2500$, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.