ABCMB: Deep Delensing Assisted Likelihood-Free Inference from CMB Polarization Maps

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.