Gravitational Wave Constraints on Einstein-ether Theory with LIGO/Virgo Data

Lorentz symmetry is a fundamental property of Einstein's theory of general relativity that one may wish to test with gravitational wave observations. Einstein-nether theory is a model that introduces Lorentzsymmetry breaking in the gravitational sector through an nether vector field, while still leading to secondorder field equations. This well-posed theory passes particle physics constraints because it modifies directly only the gravitational sector, yet it predicts deviations in the inspiral and coalescence of compact objects. We here, for the first time, put this theory to the test by comparing its gravitational wave predictions directly against LIGO/Virgo gravitational wave data. We first construct a waveform model for Einstein-nether theory, EA_IMRPhenomD_NRT, through modifications of the general relativity IMRPhenomD_NRTidalv2 model (used by the LIGO/VIRGO collaboration). This model constructs a response function that not only contains the transverse-traceless polarization but also additional Einstein-nether (scalar and vectorial) polarizations simultaneously. We then use the many current constraints on the theory to construct nontrivial priors for the Einstein-nether coupling constants. After testing the waveform model, we conduct parameter estimation studies on two gravitational wave events: GW170817 and GW190425. We find that these data are not sufficiently informative to place constraints on the theory that are stronger than current bounds from binary pulsar, Solar System, and cosmological observations. This is because, although Einstein-nether modifications include additional polarizations and have been computed beyond leading post-Newtonian order, these modifications are dominated by (already-constrained) dipole effects. These difficulties make it unclear whether future gravitational wave observations will be able to improve on current constraints on Einstein-nether theory.