Gauss-Bonnet Dark Energy and the Speed of Gravitational Waves

Gauss-Bonnet Dark Energy has been a popular model to explain the accelerated expansion of the Universe. Quite generically it also predicts the speed of gravitational waves $c_{GW}$ to be different from the speed of light. This fact alone led some authors to exclude such models in view of the new tight observational constraints on $c_{GW}$. However, the behaviour of $c_{GW}$ depends on the choice of the Gauss-Bonnet (GB) coupling function. It is possible to construct models where $c_{GW}$ is always equal to the speed of light. More generally, $c_{GW}$ is a time dependent function with instances where both speeds coincide. Nevertheless, we observe that the bound on $c_{GW}$ excludes scenarios where the GB term directly affects the expansion of the Universe, even if the constraint on the variation of the coupling function does not appear to be strong. We perform the dynamical systems analysis to see if the expansion of the Universe could be affected indirectly by modulating the behaviour of the scalar field, which modulates the GB coupling. It is shown that either the bounds on $c_{GW}$ are violated by many orders of magnitude, or it might be very difficult to find models that are consistent with other cosmological observations.