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Gravitational Waves and the Fate of Scalar-Tensor Gravity


We investigate the propagation speed of gravitational waves (GWs) in generic scalar-tensor gravity. A difference in the speed of gravity relative to the speed of light can be caused by the emergence of a disformal geometry in the gravitational sector. This requires the background scalar configuration to both spontaneously break Lorentz symmetry and couple to second derivatives of the metric perturbations through the Weyl tensor or higher derivatives of the scalar. The latter requirement allows a division of gravitational theories into two families: those that predict that GWs propagate exactly at the speed of light and those that allow for anomalous speed. Neutron star binary mergers and other GW events with an associated electromagnetic counterpart can place extremely tight constraints on the speed of GWs relative to the speed of light. However, such observations become impossible if the speed is modified too much, as predicted by some models of cosmic acceleration. Complementary measurements of the speed of gravity may be possible by monitoring nearby periodic sources, such as the binary white dwarf system WDS J0651+2844 and other eLISA verification binaries, and looking for a phase difference between the gravitational wave signal and an electromagnetic signal. Future multi-messenger GW astronomy thus has the potential to detect an anomalous speed, thereby ruling out GR and significantly changing our understanding of gravity. A negative detection will rule out or severely constrain any solution in any theory which allows for anomalous propagation of GWs.