CMB temperature lensing power reconstruction

TL;DR

This paper analyzes the biases and covariance in reconstructing the CMB lensing potential power spectrum from temperature data, highlighting the need for bias correction for accurate cosmological inference.

Contribution

It thoroughly characterizes the optimal quadratic estimator for lensing reconstruction, identifies biases at low and high multipoles, and discusses improvements to mitigate these issues.

Findings

Bias at L<250 is about 15% due to beyond-gradient terms

Full lensed trispectrum computed to fourth order explains biases

Covariance of reconstructed power shows broad correlations (~0.1%)

Abstract

We study reconstruction of the lensing potential power spectrum from CMB temperature data, with an eye to the Planck experiment. We work with the optimal quadratic estimator of Okamoto and Hu, which we characterize thoroughly in application to reconstruction of the lensing power spectrum. We find that at multipoles L<250 our current understanding of this estimator is biased at the 15% level by beyond-gradient terms in the Taylor expansion of lensing effects. We present the full lensed trispectrum to fourth order in the lensing potential to explain this effect. We show that the low-L bias, as well as a previously known bias at high-L, is relevant to the determination of cosmology and must be corrected for in order to avoid significant parameter errors. We also investigate the covariance of the reconstructed power, finding broad correlations of ~0.1%. Finally, we discuss several small improvements which may be made to the optimal estimator to mitigate these problems.