A Nearly Massless Graviton in Einstein-Gauss-Bonnet Inflation with Linear Coupling Implies Constant-roll for the Scalar Field

The striking GW170817 event indicated that the graviton is nearly massless, since the gamma rays emitted from the two neutron stars merging arrived almost simultaneously with the gravitational waves. Thus, the graviton must also be massless during the inflationary and post-inflationary era, since there is no obvious reason to believe otherwise. In this letter we shall investigate the theoretical implications of the constraint that the graviton is massless to an Einstein-Gauss-Bonnet theory with linear coupling of the scalar field to the four dimensional Gauss-Bonnet invariant. As we show, the constraint of having gravitational wave speed of the primordial gravitational waves equal to one, severely restricts the dynamics of the scalar field, imposing a direct constant-roll evolution on it. Also, as we show, the spectral index of the primordial scalar perturbations for the GW170817-compatible Einstein-Gauss-Bonnet theory with linear coupling is different in comparison to the same theory with non-linear coupling. Thus the phenomenology of the model is expected to be different, and we briefly discuss this issue too. In addition, the constant-roll condition is always related to non-Gaussianities, thus it is interesting that the imposition of a massless graviton in an Einstein-Gauss-Bonnet theory with linear coupling may lead to non-Gaussianities, so we briefly discuss this issue too.