Projected constraints on Lorentz-violating gravity with gravitational waves

Gravitational waves are excellent tools to probe the foundations of general relativity in the strongly dynamical and nonlinear regime. One such foundation is Lorentz symmetry, which can be broken in the gravitational sector by the existence of a preferred time direction and, thus, a preferred frame at each spacetime point. This leads to a modification in the orbital decay rate of binary systems, and also in the generation and chirping of their associated gravitational waves. Here we study whether waves emitted in the late, quasicircular inspiral of nonspinning, neutron star binaries can place competitive constraints on two proxies of gravitational Lorentz violation: Einstein-Æther theory and khronometric gravity. We model the waves in the small-coupling (or decoupling) limit and in the post-Newtonian approximation, by perturbatively solving the field equations in small deformations from general relativity and in the small-velocity or weak-gravity approximation. We assume that a gravitational wave consistent with general relativity has been detected with second- and third-generation, ground-based detectors, and with the proposed space-based mission DECIGO, with and without coincident electromagnetic counterparts. Without a counterpart, a detection consistent with general relativity can only place competitive constraints on gravitational Lorentz violation when using future, third-generation or space-based instruments. On the other hand, a single counterpart is enough to place constraints that are 10 orders of magnitude more stringent than current binary pulsar bounds, even when using second-generation detectors. This is because Lorentz violation forces the group velocity of gravitational waves to be different from that of light, and this difference can be very accurately constrained with coincident observations.