Spacetime symmetry breaking effects in gravitational-wave generation at the first post-Newtonian order

Current searches for signals of departures from the fundamental symmetries of general relativity using gravitational waves are largely dominated by propagation effects like dispersion and birefringence from highly dynamic sources, such as coalescing binary black holes and neutron stars. In this paper we take steps toward probing the nature of spacetime symmetries in the generation stage of gravitational waves; by using a generic effective field theory, we solve the modified Einstein equations order by order (in the coefficients for the symmetry breaking) for a generic source, and we write down the first post-Newtonian corrections, which include contributions from the spacetime symmetry breaking terms. Choosing as the source a system of point particles allows us to write down a simple toy solution explicitly, and we see that, in contrast to general relativity, the monopolar and dipolar contributions are nonvanishing. We comment on the detectability of such signals by the Laser Interferometer Space Antenna space mission, which has high signal-to-noise Galactic binaries (which can be modeled as point particles) well inside its predicted sensitivity band, sources that are inaccessible for current ground-based detectors. We also discuss the possibility of going beyond the quadrupole formula and the first post-Newtonian order, which would reveal effects that could be probed by ground-based detectors observing coalescence events.