The search for primordial gravitational waves is a central goal of cosmic microwave background (CMB) surveys. Isolating the characteristic $B$-mode polarization signal sourced by primordial gravitational waves is challenging for several reasons: the amplitude of the signal is inherently small; astrophysical foregrounds produce $B$-mode polarization contaminating the signal; and secondary $B$-mode polarization fluctuations are produced via the conversion of $E$ modes. Current and future low-noise, multi-frequency observations enable sufficient precision to address the first two of these challenges such that secondary $B$ modes will become the bottleneck for improved constraints on the amplitude of primordial gravitational waves. The dominant source of secondary $B$-mode polarization is gravitational lensing by large scale structure. Various strategies have been developed to estimate the lensing deflection and to reverse its effects the CMB, thus reducing confusion from lensing $B$ modes in the search for primordial gravitational waves. However, a few complications remain. First, there may be additional sources of secondary $B$-mode polarization, for example from patchy reionization or from cosmic polarization rotation. Second, the statistics of delensed CMB maps can become complicated and non-Gaussian, especially when advanced lensing reconstruction techniques are applied. We previously demonstrated how a deep learning network, ResUNet-CMB, can provide nearly optimal simultaneous estimates of multiple sources of secondary $B$-mode polarization. In this paper, we show how deep learning can be applied to estimate and remove multiple sources of secondary $B$-mode polarization, and we further show how this technique can be used in a likelihood analysis to produce nearly optimal, unbiased estimates of the amplitude of primordial gravitational waves.

翻译：对原始引力波的探测是宇宙微波背景（CMB）巡天的核心目标。分离由原始引力波产生的特征性$B$模偏振信号面临多重挑战：信号幅度本质微弱；天体物理前景辐射会产生污染信号的$B$模偏振；此外，$E$模的转换也会产生次级$B$模偏振涨落。当前及未来的低噪声、多频段观测已达到足够精度以应对前两项挑战，使得次级$B$模将成为提升原始引力波幅度约束的主要瓶颈。次级$B$模偏振的主要来源是大尺度结构的引力透镜效应。学界已发展多种策略来估计透镜偏折并消除其对CMB的影响，从而在原始引力波搜寻中降低透镜$B$模造成的混淆。然而，仍存在若干复杂问题：首先，可能存在其他次级$B$模偏振源，例如不均匀再电离或宇宙偏振旋转；其次，去透镜后的CMB图统计特性会变得复杂且非高斯，尤其在应用先进透镜重构技术时。我们先前已证明深度学习网络ResUNet-CMB能够近乎最优地同步估计多种次级$B$模偏振源。本文展示如何应用深度学习来估计并消除多种次级$B$模偏振源，并进一步说明该技术如何用于似然分析，以产生近乎最优且无偏的原始引力波幅度估计。