Approximate Likelihood Approaches for Detecting the Influence of Primordial Gravitational Waves in Cosmic Microwave Background Polarization

TL;DR

This paper introduces a novel likelihood method for estimating the primordial gravitational wave signal in CMB polarization data, effectively combining full likelihood analysis with quadratic delensing to improve detection accuracy.

Contribution

It presents a pixel space, all-order likelihood approach that incorporates all lensing effects and anomalies, enhancing the precision of tensor-to-scalar ratio estimation in future CMB experiments.

Findings

Efficient computation of the full Gaussian likelihood profile as a function of r.

Improved delensing technique that accounts for all order lensing effects.

Enhanced accuracy in detecting primordial B-mode signals.

Abstract

One of the major targets for next-generation cosmic microwave background (CMB) experiments is the detection of the primordial B-mode signal. Planning is under way for Stage-IV experiments that are projected to have instrumental noise small enough to make lensing and foregrounds the dominant source of uncertainty for estimating the tensor-to-scalar ratio $r$ from polarization maps. This makes delensing a crucial part of future CMB polarization science. In this paper we present a likelihood method for estimating the tensor-to-scalar ratio $r$ from CMB polarization observations, which combines the benefits of a full-scale likelihood approach with the tractability of the quadratic delensing technique. This method is a pixel space, all order likelihood analysis of the quadratic delensed B modes, and it essentially builds upon the quadratic delenser by taking into account all order lensing and pixel space anomalies. Its tractability relies on a crucial factorization of the pixel space covariance matrix of the polarization observations which allows one to compute the full Gaussian approximate likelihood profile, as a function of $r$, at the same computational cost of a single likelihood evaluation.