Tests of weak equivalence principle with the gravitational wave signals in the LIGO-Virgo catalog GWTC-1

Shu-Cheng Yang, Wen-Biao Han, Gang Wang

The weak equivalence principle (WEP) is the cornerstone of gravitational theories. At the local scale, WEP has been tested to high accuracy by various experiments \cite{will2014confrontation,touboul2017microscope}. On the intergalactic distance scale, WEP could be tested by comparing the arrival time of different messengers emitted from the same source\cite{krauss1988test,longo1988new,wei2015testing}. The gravitational time delay caused by massive galaxies is proportional to $\gamma+1$, where the parameter $\gamma$ is unity in general relativity. The values of $\gamma$ for different massless particles should be different if WEP is violated, i.e., $\Delta \gamma$ is used to indicate the deviation from WEP. So far, $|\Delta \gamma|$ has been constrained to $\sim 10^{-10}$ with gamma-ray bursts, fast radio bursts and gravitational waves \cite{wei2017multimessenger}. Here we report a new estimation of $|\Delta \gamma|$ by using the gravitational wave (GW) data of binary black hole (BBH) coalescences in the LIGO-Virgo catalog GWTC-1 \cite{abbott2019gwtc}. Our results show that $|\Delta \gamma|$ is not larger than $7.9\times 10^{{-15}^{+2.6}_{-3.0}}$ at 90\% confidence level for uniform logarithmic prior. For an alternative prior, the 90\% confidence interval of $\Delta \gamma$ is $[{-1.0\times 10^{-15}},~+1.4\times 10^{-17}]$. WEP may be obeyed on the intergalactic distance scale for GWs.