Effect of lensing non-Gaussianity on the CMB power spectra

TL;DR

This paper calculates the small but precise correction to CMB power spectra caused by non-Gaussian lensing deflections, finding it negligible for current and near-future observations.

Contribution

It provides the first leading-order calculation of non-Gaussian lensing effects on CMB power spectra, including an analytic model for the skewness signal.

Findings

Leading correction to polarization spectra is about 0.3%.

Higher-order Gaussian smoothing reduces the effect on EE spectra.

Non-Gaussian effects are negligible for foreseeable future observations.

Abstract

Observed CMB anisotropies are lensed, and the lensed power spectra can be calculated accurately assuming the lensing deflections are Gaussian. However, the lensing deflections are actually slightly non-Gaussian due to both non-linear large-scale structure growth and post-Born corrections. We calculate the leading correction to the lensed CMB power spectra from the non-Gaussianity, which is determined by the lensing bispectrum. The lowest-order result gives $\sim 0.3\%$ corrections to the BB and EE polarization spectra on small-scales, however we show that the effect on EE is reduced by about a factor of two by higher-order Gaussian lensing smoothing, rendering the total effect safely negligible for the foreseeable future. We give a simple analytic model for the signal expected from skewness of the large-scale lensing field; the effect is similar to a net demagnification and hence a small change in acoustic scale (and therefore out of phase with the dominant lensing smoothing that predominantly affects the peaks and troughs of the power spectrum).