The direct detection of gravitational waves (GWs) is an invaluable new tool to probe gravity and the nature of cosmic acceleration. A large class of scalar-tensor theories predicts that GWs propagate with velocity different than the speed of light, a difference that can be $\mathcal{O}(1)$ for many models of dark energy. We determine the conditions behind the anomalous GW speed, namely, that the scalar field spontaneously breaks Lorentz invariance and couples to the metric perturbations via the Weyl tensor. If these conditions are realized in nature, the delay between GW and electromagnetic signals from distant events will run beyond human time scales, making it impossible to measure the speed of GWs using neutron star mergers or other violent events. We present a robust strategy to exclude or confirm an anomalous speed of GWs using eclipsing binary systems, the electromagnetic phase of which can be exquisitely determined. The white dwarf binary $\mathrm{J}0651+2844$ is a known example of such a system that can be used to probe deviations in the GW speed as small as $c_g/c-1\gtrsim 2\times {10}^{-12}$ when LISA comes online. This test will either eliminate many contender models for cosmic acceleration or wreck a fundamental pillar of general relativity.

• Received 23 August 2016

DOI:https://doi.org/10.1103/PhysRevD.95.084029