Statistical Methods for Detection of Primordial Gravitational Waves

随着LIGO引力波天文台在2016年初宣布的探测，人们期待已久的引力波天文学时代开始了。科学家现在可以非常直接地在极端条件下探索自然，比如合并黑洞或中子星。宇宙学家打算使用引力波来深入探索大爆炸的最早时刻。宇宙学家没有监测LIGO探测器4公里长手臂长度的变化，而是在宇宙微波背景(CMB)中寻找引力波对偏振模式的印记。CMB是一种光，在很大程度上，这种光最后一次与物质相互作用是在宇宙只有几十万年的时候。如果在早期宇宙中产生密度扰动的最简单和最成功的经验情景是正确的，那么所产生的信号应该是可观察到的。这样的探测将打开一个新的、更直接的窗口，了解这个超早期时代，以及我们第一个关于引力场量子力学方面的实验探测器，并允许我们测试关于我们宇宙中空间结构(密度不均匀)起源的理论。为了达到对原始引力波(PGW)的敏感性，目前正在规划阶段(如IV阶段)的实验目标。(实验)，需要开发新的统计工具--特别是用于量化污染物对感兴趣信号的去除的不确定性。这个项目将直接解决这些统计挑战，重点关注在CMB中探测原始引力波的两个主要障碍：引力透镜的污染和我们银河系星际介质的毫米波辐射。拟议工作产生的统计方法不仅将使一些非常令人兴奋的科学成为可能，而且还将为与大型空间数据集相关的广泛的统计问题提供信息。该项目直接解决了与探测宇宙微波背景(CMB)中的原始引力波有关的两个主要统计挑战：引力透镜的污染和我们银河系星际介质发射的毫米波辐射。该项目的第一部分是使用一种新的再参数化技术和一种专门为克服吉布斯采样器与CMB脱胶相关的缓慢混合而专门设计的人工消相干技术来开发脱胶问题的全面贝叶斯解决方案。使用透镜如何在CMB偏振中对E模和B模进行混叠的物理原理，这种定制的重新参数化可以表现出用于E模的充分参数化和用于偏振B模的辅助参数的属性。这对于主Gibbs链的快速混合和对于贝叶斯去噪的哈密顿马尔可夫链的高接受率是至关重要的。该项目的第二个主要部分直接处理与前景污染物有关的挑战：特别是量化通过观测传播的不确定性，以及从原始引力波估计的B型波动。该项目将侧重于开发非平稳性和非高斯性的新随机场模型，目的是量化不确定性，而不是估计和随后消除前景排放。由此产生的模型和技术也将为与非平稳随机场模型和非高斯空间随机场的分层建模相关的一般统计应用提供信息。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

With the detections by the LIGO gravitational wave observatories announced in early 2016 the long-awaited era of gravitational wave astronomy has begun. Scientists can now very directly explore nature under extreme conditions such as those that occur with merging black holes or neutron stars. Cosmologists intend to use gravitational waves to probe deep into the earliest moments of the big bang. Rather than monitoring changes to the lengths of the 4km-long arms of the LIGO detectors, cosmologists are seeking the imprint of gravitational waves on polarization patterns in the cosmic microwave background (CMB) -- light that, for the most part, last interacted with matter when the universe was just a few hundred thousand years old. If the simplest and most empirically successful scenario for the generation of density perturbations in the early universe is correct, the resulting signal should be observable. Such a detection would open up a new, and more direct, window on this ultra-early epoch as well as our first experimental probe of quantum-mechanical aspects of the gravitational field and allow us to test theories of the origin of spatial structure (density inhomogeneities) in our universe. To achieve the sensitivity to primordial gravitational waves (PGWs), being targeted by experiments in the planning stages now (such as the ?Stage IV? experiment), requires the development of new statistical tools -- in particular for the quantification of uncertainties in the removal of contaminants to the signal of interest. This project will directly address these statistical challenges by focusing on the two main obstacles for the detection of primordial gravitational waves in the CMB: contamination from gravitational lensing and millimeter wavelength radiation from the interstellar medium in our own galaxy. The statistical methodology resulting from the proposed work will not only enable some very exciting science, but also inform a broad range of statistical problems associated with large spatial datasets. This project directly addresses the two main statistical challenges associated with the detection of primordial gravitational waves in the cosmic microwave background (CMB): contamination from gravitational lensing and the emission of millimeter wavelength radiation from the interstellar medium in our own galaxy. The first part of the project is the development of a full-scale Bayesian solution to the delensing problem using a new re-parameterization technique derived from a dynamical systems characterization of delensing and an artificial decoherence technique specifically designed to overcome the slow mixing of Gibbs samplers associated with CMB delensing. This custom re-parameterization, using the physics of how lensing aliases E-modes and B-modes in the CMB polarization, can exhibit properties of both a sufficient parametrization for the E-mode and an ancillary parameterization for the polarization B-mode. This is crucial for fast mixing of the main Gibbs chain and for high acceptance rates of Hamiltonian Markov chains for Bayesian delensing. The second main part of the project directly addresses the challenges associated with foreground contaminants: in particular the quantification of uncertainty that propagates through the observations to the estimated B-mode fluctuations from primordial gravitational waves. The project will focus on developing new random field models of the non-stationarity and non-Gaussianity aimed at quantifying uncertainty rather than the estimation, and subsequent removal, of foreground emission. The resulting models and techniques will also inform general statistical applications associated with non-stationary random field models and the hierarchical modeling of non-Gaussian spatial random fields.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.