Non-Minimally Coupled Einstein Gauss Bonnet Inflation Phenomenology in View of GW170817

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We study the inflationary phenomenology of a non-minimally coupled Einstein Gauss-Bonnet gravity theory, in the presence of a scalar potential, under the condition that the gravitational wave speed of the primordial gravitational waves is equal to unity, that is $c_T^2=1$, in natural units.

• The equations of motion, which are derived directly from the gravitational action, form a system of differential equations with respect to Hubble's parameter and the inflaton field which are very complicated and cannot be solved analytically, even in the minimal coupling case.
• In this paper, we present a variety of different approximations which could be used, along with the constraint $c_T^2=1$, in order to produce an inflationary phenomenology compatible with recent observations.
• All the different approaches are able to lead to viable results if the model coupling functions obey simple relations, however, different approaches contain different approximations which must be obeyed during the first horizon crossing, in order for the model to be rendered correct.