GravitaS · The gravitational S-matrix: from theory to experiment

Recent insights into the gravitational S-matrix, which describes the scattering of gravitating particles, have lead to a breakthrough in the perturbative understanding of the two-body problem in General Relativity, with direct relevance to gravitational wave physics. Such advances have been enabled by the methods of scattering amplitudes and effective field theory, originally developed in the context of particle and collider physics. Despite recent progress, a formalism to extract the dynamics of inspiralling compact binaries from scattering amplitudes is still lacking, in order for the results of this program to be fully implemented in the analysis of gravitational wave data. Furthermore, the advent of space-based detectors will enable the observation of extreme-mass-ratio binary systems, and push gravitational wave astronomy into the strong-field regime not amenable to traditional perturbative methods.We propose to address these challenges by breaking new ground and extending the reach of the gravitational S-matrix program by integrating insights from gravitational self-force theory, which solves the dynamics order-by-order in the mass ratio of the binary. We focus on three objectives: 1. Use the scattering of gravitational waves off a compact objects to extract universal predictions and extend the methods of scattering amplitudes beyond the weak-field regime.2. Develop a new approach to predicting the scattering dynamics of extreme-mass-ratio binaries leveraging recent advances in scattering amplitudes and self-force theory.3. Design a framework to translate observables from the scattering of binaries to the bound dynamics relevant for experiment, utilizing insights from effective field theory.The successful completion of this program will fundamentally reshape our understanding of gravitational scattering and the dynamics of compact binary systems, and revolutionize our ability to make predictions for current and future gravitational wave observatories.