Gauss-Bonnet Dark Energy and the speed of gravitational waves

Abstract

Gauss-Bonnet Dark Energy has been a popular model to explainthe accelerated expansion of the Universe. Quite generically it alsopredicts the speed of gravitational waves c GW to be differentfrom the speed of light. This fact alone led some authors to excludesuch models in view of the new tight observational constraints on c GW. However, the behaviour of c GW depends on the choice ofthe Gauss-Bonnet (GB) coupling function. It is possible to constructmodels where c GW is always equal to the speed of light. More generally, c GW is a time dependent function with instances where both speedscoincide. Nevertheless, we observe that the bound on c GW excludesscenarios where the GB term directly affects the expansion of theUniverse, even if the constraint on the variation of the couplingfunction does not appear to be strong. We perform the dynamical systemsanalysis to see if the expansion of the Universe could be affectedindirectly by modulating the behaviour of the scalar field, whichmodulates the GB coupling. It is shown that either the bounds on c GWare violated by many orders of magnitude, or it might be very difficultto find models that are consistent with other cosmological observations.