Bounding the Speed of Gravity with Gravitational Wave Observations

The time delay between gravitational wave signals arriving at widely separated detectors can be used to place upper and lower bounds on the speed of gravitational wave propagation. Using a Bayesian approach that combines the first three gravitational wave detections reported by the LIGO Scientific and Virgo Collaborations we constrain the gravitational waves propagation speed $c_{\mathrm{gw}}$ to the 90% credible interval $0.55c<c_{\mathrm{gw}}<1.42c$, where $c$ is the speed of light in vacuum. These bounds will improve as more detections are made and as more detectors join the worldwide network. Of order 20 detections by the two LIGO detectors will constrain the speed of gravity to within 20% of the speed of light, while just five detections by the LIGO-Virgo-Kagra network will constrain the speed of gravity to within 1% of the speed of light.

Figure 1

Posterior distributions for the gravitational wave propagation speed derived from each of the individual LIGO events for prior distributions uniform in $c_{\mathrm{gw}}$ or $\ln c_{\mathrm{gw}}$.

Figure 2

Posterior distributions for the gravitational wave propagation speed derived by combining the first three LIGO detections. Prior distributions uniform in $c_{\mathrm{gw}}$ or uniform in $\ln c_{\mathrm{gw}}$ were considered, with the interval starting at either $c_{\mathrm{L}}=c/100$ or $c_{\mathrm{L}}=c$.

Figure 3

Slices through the joint electromagnetic time delay distribution for the $HLVK$ network using Hanford as the reference site. Darker colors in the two-dimensional slices indicate higher density. Note the cuplike structure of the distributions (higher at the edges than in the center).