A dimension-six Lorentz-violating gravity operator is linearized to obtain gravitational-wave dispersion relations, and time-of-flight data from GW170817 and GW150914 bound the coefficients to 10^-5 to 10^-4 m^2 (nonbirefringent) and 10^-10 to 10^-8 m^2 (birefringent).
Modifications to Plane Gravitational Waves from Minimal Lorentz Violation
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General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the modifications to the two gravitational wave modes from the minimal Lorentz-violation coupling. The perturbation solution for the metric fluctuation up to the first order in Lorentz violation is discussed. Then, we investigate the motions of test particles under the influence of the plane gravitational waves with Lorentz violation. First-order deviations from the usual motions are found.
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New constraints on modified gravity with dimension-six operators from gravitational waves
A dimension-six Lorentz-violating gravity operator is linearized to obtain gravitational-wave dispersion relations, and time-of-flight data from GW170817 and GW150914 bound the coefficients to 10^-5 to 10^-4 m^2 (nonbirefringent) and 10^-10 to 10^-8 m^2 (birefringent).