Optimal constraints on primordial gravitational waves from the lensed CMB

TL;DR

This paper develops an optimal estimator for primordial gravitational waves from lensed CMB data, demonstrating its effectiveness and near-optimal performance on simulated low-noise polarization data, promising improved constraints for future experiments.

Contribution

The paper introduces a new optimal estimator for the tensor-to-scalar ratio in lensed CMB data, combining fast lensing reconstruction with optimal recovery, and demonstrates its near-optimal performance on simulations.

Findings

The estimator is unbiased and optimal for simulated data.

Iterative delensing improves constraints by less than 10%.

The method is promising for stage IV CMB experiments.

Abstract

We demonstrate how to obtain optimal constraints on a primordial gravitational wave component in lensed Cosmic Microwave Background (CMB) data under ideal conditions. We first derive an estimator of the tensor-to-scalar ratio, $r$, by using an error-controlled close approximation to the exact posterior, under the assumption of Gaussian primordial CMB and lensing deflection potential. This combines fast internal iterative lensing reconstruction with optimal recovery of the unlensed CMB. We evaluate its performance on simulated low-noise polarization data targeted at the recombination peak. We carefully demonstrate our $r$-posterior estimate is optimal and shows no significant bias, making it the most powerful estimator of primordial gravitational waves from the CMB. We compare these constraints to those obtained from $B$-mode band-power likelihood analyses on the same simulated data, before and after map-level quadratic estimator delensing, and iterative delensing. Internally, iteratively delensed band powers are only slightly less powerful on average (by less than 10\%), promising close-to-optimal constraints from a stage IV CMB experiment.