Compact binary systems in the post-Newtonian limit of gravitational theories with preferred frames
Gravitational-wave observations of compact-binary inspirals offer the opportunity to test deviations from general relativity in both strong and weak-field regimes. In previous work, we developed a theory-independent formalism for describing compact-binary dynamics in metric theories of gravity without preferred frames, using the parametrised post-Newtonian (PPN) couplings together with an additional set of scalar sensitivity parameters that encode violations of the strong equivalence principle. Here, we extend this framework to include preferred-frame effects, of the type that can arise in (for example) vector-tensor theories of gravity. This is achieved by introducing a time-like vector field that identifies the preferred frame, and then by allowing compact body masses to depend on the invariant formed from this field and the body's four-velocity. We calculate the modified equation of motion up to first post-Newtonian order (1PN), where the preferred-frame PPN parameters $α_1$ and $α_2$ acquire contributions from our new vector sensitivities. We further combine scalar and vector sensitivities in a unified formalism, which we validate with an example scalar-vector-tensor theory. This approach provides the orbital dynamics required to extend gravitational-wave constraints on PPN and sensitivity parameters to theories of gravity that admit preferred frames, as well as those that do not.