Impact of next-to-leading order contributions to CMB lensing

TL;DR

This paper investigates how higher-order lensing effects, including post-Born corrections and large-scale structure influences, affect the accuracy of cosmological parameter estimation from CMB data, emphasizing their importance for future surveys.

Contribution

It quantifies the impact of next-to-leading order lensing corrections on key cosmological parameters, highlighting the necessity to include these effects in analyses for precise results.

Findings

Neglecting higher-order lensing can mimic a primordial tensor-to-scalar ratio of about 10^{-3}.

Higher-order lensing causes a nearly two sigma shift in N_eff for future surveys.

Post-Born and LSS effects significantly influence polarization spectra analysis.

Abstract

In this Letter we study the impact on cosmological parameter estimation, from present and future surveys, due to lensing corrections on CMB temperature and polarization anisotropies beyond leading order. In particular, we show how post-Born corrections, LSS effects and the correction due to the change in the polarization direction between the emission at the source and the detection at the observer, are non-negligible in the determination of the polarization spectra. They have to be taken into account for an accurate estimation of cosmological parameters sensitive to or even based on these spectra. We study in detail the impact of higher order lensing on the determination of the tensor-to-scalar ratio $r$ and on the estimation of the effective number of relativistic species $N_\text{eff}$. We find that neglecting higher order lensing terms can lead to misinterpreting these corrections as a primordial tensor-to-scalar ratio of about $\mathcal{O}(10^{-3})$. Furthermore, it leads to a shift of the parameter $N_\text{eff}$ by nearly two sigma considering the level of accuracy aimed by future S4 surveys.