On likelihood-based analysis of the gravitationally (de)lensed CMB

TL;DR

This paper develops optimal likelihood-based methods for de-lensing the CMB to improve information extraction, compares them with quadratic estimators, and suggests pathways for advancing beyond-QE techniques.

Contribution

It derives optimal data compression statistics for the lensed CMB and clarifies their relation to quadratic estimators, proposing improvements and future directions.

Findings

Optimal data compression statistics for lensed CMB derived

Clarification of the role of terms in quadratic estimator framework

Proposed improvements for practical de-lensing implementations

Abstract

By reducing variance induced by gravitational lensing, likelihood-based de-lensing techniques have true potential to extract significantly more information from deep and high-resolution Cosmic Microwave Background (CMB) data than traditional methods. We derive here optimal data compression statistics for the lensed CMB, and clarify the role of each term, demonstrating their direct analogs in the quadratic estimator (QE) framework. We discuss in this light pros and cons of practical implementations, including the MUSE approach, as used in the latest SPT-3G cosmological analysis, and give improvements. We discuss pathways for porting the large robustness and redundancy toolbox of the QE approach to beyond-QE with simple means.