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.

翻译：原初引力波背景（PGWB）的存在是暴胀宇宙学的一个稳健预言，但迄今尚未被发现。其探测最有希望的途径是通过宇宙微波背景（CMB）$B$模式偏振的测量。然而，这并非易事，原因在于：（a）CMB图会受到引力透镜效应的扭曲；（b）CMB数据的高维特性使得基于似然的分析方法计算成本极高。本文提出一种高效的无似然端到端推断方法，可直接从斯托克斯偏振参数$Q$和$U$的透镜化图中推断张标比$r$的后验分布。我们的方法采用生成模型对图像进行去透镜处理，并利用近似贝叶斯计算（ABC）算法对$r$进行采样。我们证明，该方法能产生$r$的无偏估计，且具有校准良好的不确定性量化。