Propagation of Gravitational Waves in Einstein--Gauss-Bonnet Gravity for Cosmological and Spherically Symmetric Spacetimes

In this work, we examine the propagation of gravitational waves in cosmological and astrophysical spacetimes in the context of Einstein--Gauss-Bonnet gravity, in view of the GW170817 event. The perspective we approach the problem is to obtain a theory which can produce a gravitational wave speed that is equal to that of light in the vacuum, or at least the speed can be compatible with the constraints imposed by the GW170817 event. As we show, in the context of Einstein--Gauss-Bonnet gravity, the propagation speed of gravity waves in cosmological spacetimes can be compatible with the GW170817 event, and we reconstruct some viable models. However, the propagation of gravity waves in spherically symmetric spacetimes violates the GW170817 constraints, thus it is impossible for the gravitational wave that propagates in a spherically symmetric spacetime to have a propagating speed which is equal to that of light in the vacuum. The same conclusion applies to the Einstein--Gauss-Bonnet theory with two scalars. We discuss the possible implications of our results on spherically symmetric spacetimes.