Full covariance of CMB and lensing reconstruction power spectra

TL;DR

This paper analyzes the full covariance between CMB and lensing reconstruction power spectra, highlighting how their correlations impact parameter estimation and proposing methods to mitigate these effects for future CMB observations.

Contribution

It provides a comprehensive analysis of auto- and cross-covariances, including polarization, and demonstrates how to effectively model and reduce these correlations in CMB-S4 data.

Findings

Correlations are detectable at ~5σ in CMB-S4.

Realization-dependent subtraction reduces covariance complexity.

Neglecting correlations can underestimate parameter errors by tens of percent.

Abstract

CMB and lensing reconstruction power spectra are powerful probes of cosmology. However they are correlated, since the CMB power spectra are lensed and the lensing reconstruction is constructed using CMB multipoles. We perform a full analysis of the auto- and cross-covariances, including polarization power spectra and minimum variance lensing estimators, and compare with simulations of idealized future CMB-S4 observations. Covariances sourced by fluctuations in the unlensed CMB and instrumental noise can largely be removed by using a realization-dependent subtraction of lensing reconstruction noise, leaving a relatively simple covariance model that is dominated by lensing-induced terms and well described by a small number of principal components. The correlations between the CMB and lensing power spectra will be detectable at the level of $\sim 5\sigma$ for a CMB-S4 mission, and neglecting those could underestimate some parameter error bars by several tens of percent. However we found that the inclusion of external priors or data sets to estimate parameter error bars can make the impact of the correlations almost negligible.