Astrophysics and Cosmology with the Mass Distribution of Gravitational Wave Sources

Since the first direct detection of gravitational waves (GWs) just under 10 years ago, astronomers and physicists have gained immense physical insight by analyzing the individual compact binary coalescences (CBCs) from which GWs arise. Now, more than 90 GW detections have been published, and the most sensitive network of GW detectors is in observing mode and has produced over 200 additional public GW detection candidates so far. The rapidly-growing catalog of GW detections means that GW astronomy is firmly in the population era, where we stand to gain more physical insight by analyzing the ensemble of GW detections than any one source alone. This dissertation focuses on extracting physical information from one dimension of the GW source population: the mass distribution of CBCs. The first part of the dissertation introduces GW cosmology and GW astrophysics and describes the statistical methods used to infer the population of CBC from GW data. The second part of the dissertation applies this method to identify and characterize features in the mass distribution of CBCs. We search for imprints of nuclear physics and the supernova explosion mechanism in the low-mass region of the mass distribution, finding evidence of the former and hints of the latter. We then assess the robustness of features in the high-mass region that were originally found using a flexible, rather than astrophysically-informed, search. We find that only two of the previously-identified features are statistically robust. The third part of the dissertation applies the features found in the second part to open problems in astrophysics: the stellar origin of CBC and the Hubble tension. We demonstrate that comparing features in the distributions of primary and secondary black hole masses can aid in determining whether CBCs are mostly formed through dynamical encounters in dense stellar environments, or if they originate as binary star systems in the comparably diffuse galactic field. However, we show that such knowledge of the processes that produce CBCs is not necessary in order to use mass distribution features to measure the expansion rate of the Universe. The final part of the dissertation discusses the scenario in which population models do not describe all of the data, or when they are significantly altered by a single GW event. We demonstrate how to identify such outliers to the inferred CBC population, and apply this to current GW catalogs.