Testing Einstein’s weak equivalence principle with gravitational waves

A conservative constraint on Einstein’s weak equivalence principle (WEP) can be obtained under the assumption that the observed time delay between correlated particles from astronomical sources is dominated by the gravitational fields through which they move. Current limits on the WEP are mainly based on the observed time delays of photons with different energies. It is highly desirable to develop more accurate tests that include the gravitational wave (GW) sector. The detection by the advanced LIGO/VIRGO systems of gravitational waves will provide attractive candidates for constraining the WEP, extending the tests to gravitational interactions with potentially higher accuracy. Considering the capabilities of the advanced LIGO/VIRGO network and the source direction uncertainty, we show that the joint detection of GWs and electromagnetic signals could probe the WEP to an accuracy down to ${10}^{-10}$, which is one order of magnitude tighter than previous limits, and 7 orders of magnitude tighter than the multimessenger (photons and neutrinos) results by supernova 1987A.

Figure 1

Expected limits on the differences of the $\gamma$ values between the GW signals and the photons for various types of EM counterparts. The vertical lines correspond to different characteristic times.