AB$\mathbb{C}$MB: Deep Delensing Assisted Likelihood-Free Inference from CMB Polarization Maps

TL;DR

This paper presents a novel likelihood-free inference approach using deep learning and ABC to estimate the tensor-to-scalar ratio from lensed CMB polarization maps, improving efficiency and accuracy in primordial gravitational wave detection.

Contribution

It introduces a deep delensing method combined with ABC for direct, unbiased inference of the tensor-to-scalar ratio from CMB polarization data, addressing computational challenges.

Findings

Unbiased estimates of r with calibrated uncertainties.

Efficient likelihood-free inference from high-dimensional CMB data.

Effective delensing of polarization maps using a generative model.

Abstract

The existence of a cosmic background of primordial gravitational waves (PGWB) is a robust prediction of inflationary cosmology, but it has so far evaded discovery. The most promising avenue of its detection is via measurements of Cosmic Microwave Background (CMB) $B$-polarization. However, this is not straightforward due to (a) the fact that CMB maps are distorted by gravitational lensing and (b) the high-dimensional nature of CMB data, which renders likelihood-based analysis methods computationally extremely expensive. In this paper, we introduce an efficient likelihood-free, end-to-end inference method to directly infer the posterior distribution of the tensor-to-scalar ratio $r$ from lensed maps of the Stokes $Q$ and $U$ polarization parameters. Our method employs a generative model to delense the maps and utilizes the Approximate Bayesian Computation (ABC) algorithm to sample $r$. We demonstrate that our method yields unbiased estimates of $r$ with well-calibrated uncertainty quantification.