Statistical Methods for Detection of Primordial Gravitational Waves

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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.