The mergers of black holes and/or neutron stars in binary systems produce the most extreme gravitational environments in the local universe. The first direct detections of gravitational waves by Advanced LIGO and Virgo provide unprecedented observational access to the highly dynamical, strong-curvature regime of gravity. These measurements allow us to test Einstein’s theory of General Relativity in this extreme regime. This thesis examines how the gravitational-wave signal produced during the inspiral—the earliest phase of a binary’s coalescence—can better inform our understanding of the fundamental nature of gravity.

My work addressing this topic is comprised of two major components. First, I examine the behavior of binary black-hole and neutron-star systems in various possible extensions of General Relativity, constructing analytic models of their orbital motion and gravitational waveform—their gravitational-wave signature—during their inspiral. The majority of alternative theories I consider modify General Relativity by introducing a new scalar component of gravity. In many of these theories, standard perturbative techniques are used to model the inspiral of binary systems. However, I also examine in depth the non-perturbative phenomenon of scalarization for which such methods fail. I show that this phenomenon occurs due to a second-order phase transition in the strong-gravity regime and develop an analytic framework to model the effect across a range of alternative theories of gravity.

The other component of this thesis is the development of a statistical infrastructure suitable for testing General Relativity using gravitational-wave observations. I adopt a more flexible and modular approach than existing alternatives, allowing this infrastructure to be immediately applied with a wide range of waveform models. In work done in conjunction with the LIGO Scientific and Virgo Collaborations, I use this statistical framework to place bounds on phenomenological deviations from General Relativity using the binary black-hole and neutron-star events detected during LIGO’s first and second observing runs—no evidence for deviations from Relativity is found.

These two research directions outlined above are complementary; the type of statistical inference discussed here requires models for the gravitational-wave signal produced by inspiraling systems that allow for deviations from General Relativity, and the analytic models I construct are suitable for this task. In this thesis, I carry out the complete procedure of building and employing analytic models of gravitational waveforms to place constraints on specific alternative theories of gravity with observations by LIGO and Virgo.