Probing Astrophysics and Fundamental Physics with Accurate Gravitational Waveforms for Eccentric Compact Binary Inspirals

The growing number of gravitational wave observations suggests the possibility of detecting signals from binaries with non-negligible orbital eccentricity in the near future. Models that incorporate the effects of small eccentricities ($e < 0.2$) exit, but they may not be sufficient to analyze waves from systems with moderate eccentricity. We recently developed a model that faithfully accounts for eccentric corrections in the moderate eccentricity regime ($e < 0.8$ for certain source masses) at 3rd post-Newtonian order. In this talk, I will first review the waveform construction, and then focus on the astrophysical and fundamental physics that can be probed if we detect such eccentric signal, based on a Bayesian parameter estimation study. I will first discuss the accuracy to which eccentricity can be measured given a moderately eccentric signal, as well as the smallest eccentricity that can be measured given a slightly eccentric signal, and the systematic biases that can be incurred if a quasi-circular model is used to extract an eccentric signal. I will conclude with a discussion of how eccentricity enhances our ability to test General Relativity, focusing on tests of scalar-tensor theory and Einstein-dilaton-Gauss-Bonnet gravity.