Gravitational waves from the quasicircular inspiral of compact binaries in Einstein-aether theory

We study gravitational waves emitted by a binary system of nonspinning bodies in a quasicircular inspiral within the framework of Einstein-aether theory. In particular, we compute explicitly and analytically the expressions for the time-domain and frequency-domain waveforms, gravitational wave polarizations, and response functions for both ground- and space-based detectors in the post-Newtonian approximation. We find that, when going beyond the leading order in the post-Newtonian approximation, the non-Einsteinian polarization modes contain terms that depend on both the first and the second harmonics of the orbital phase. We also calculate analytically the corresponding parametrized post-Einsteinian parameters, generalizing the existing framework to allow for different propagation speeds among the scalar, vector, and tensor modes, without assumptions about the magnitude of its coupling parameters, and meanwhile, allowing the binary system to have relative motions with respect to the aether field. Such results allow for the easy construction of Einstein-aether templates that could be used in Bayesian tests of general relativity in the future.