Cosmic microwave background lensing with optimal convergence and shear estimators

TL;DR

This paper develops optimal estimators for cosmic microwave background lensing that improve reconstruction accuracy by generalizing previous methods and enabling internal consistency checks, with potential applications to polarization data.

Contribution

It introduces a generalized, optimal approach to convergence and shear estimators for CMB lensing, extending beyond the squeezed limit and allowing for better separation of lensing effects.

Findings

Establishes optimal convergence and shear estimators from the temperature field.

Provides a method to separate lensing from non-lensing modes.

Potential to enhance polarization lensing reconstruction.

Abstract

We present the optimal convergence and shear estimators for lensing reconstruction from the cosmic microwave background temperature field. This generalizes the deflection estimator, is sensitive to non-lensing modes, provides internal consistency checks, and is always at least as optimal. Previously, these estimators were only known in the squeezed limit. This paper decomposes convergence and shear fields into cosine and sine waves and the lensed correlation function is then Taylor expanded in the wave amplitudes. Maximizing the likelihood function gives the optimal estimators for the convergence and shear fields. This method has the potential to improve the lensing reconstruction of the cosmic microwave background polarization field: the shear and convergence can be optimally combined to form a deflection estimator, or used separately to separate non-lensing modes, or utilize lensing of non-Gaussian secondary foregrounds.