Constraining the propagation speed of gravitational waves with compact binaries at cosmological distances

When testing gravity in a model-independent way, one of the crucial tests is measuring the propagation speed of a gravitational wave (GW). In general relativity, a GW propagates with the speed of light, while in the alternative theories of gravity, the propagation speed could deviate from the speed of light due to the modification of gravity or spacetime structure at a quantum level. Previously, we proposed a method to measure the GW speed by directly comparing the arrival times between a GWand a photon from the binary merger of neutron stars or a neutron star and black hole, assuming that it is associated with a short gammaray burst. The sensitivity is limited by the intrinsic time delay between a GW and a photon at the source. In this paper, we extend the method to distinguish the intrinsic time delay from the true signal caused by anomalous GW speed with multiple events at cosmological distances, considering the redshift distribution of GW sources, redshift-dependent GW propagation speed, and the statistics of intrinsic time delays. We show that an advanced GW detector such as the Einstein Telescope will be able to robustly constrain the GW propagation speed at a precision of ∼10−16. We also discuss the optimal statistic to measure the GW speed by performing numerical simulations.