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

TL;DR

This paper proposes an extended method using multiple cosmological gravitational wave events to precisely measure the GW propagation speed, aiming to distinguish intrinsic delays from true speed deviations, with potential constraints at the level of 10^{-16}.

Contribution

It introduces a novel approach combining multiple GW events and redshift information to improve constraints on GW speed beyond previous single-event methods.

Findings

Advanced detectors can constrain GW speed to ~10^{-16}

Method effectively separates intrinsic delays from true speed deviations

Numerical simulations validate the optimal statistical approach

Abstract

In testing gravity a model-independent way, one of 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 the method measuring the GW speed by directly comparing the arrival times between a GW and a photon from the binary merger of neutron stars or neutron star and black hole, assuming that it is associated with a short gamma-ray 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, also 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 Einstein Telescope will constrain the GW propagation speed at the precision of ~10^{-16}. We also discuss the optimal statistic to measure the GW speed, performing numerical simulations.