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

TL;DR

This paper investigates inflationary models within non-minimally coupled Einstein Gauss-Bonnet gravity, ensuring compatibility with gravitational wave speed constraints from GW170817, and explores various approximations to match observational data.

Contribution

It introduces multiple approximation methods for analyzing complex inflationary equations in Einstein Gauss-Bonnet gravity under GW speed constraints, expanding the understanding of viable models.

Findings

Viable inflationary models compatible with GW170817 constraints.

Different approximation approaches can produce consistent phenomenology.

Certain models are non-viable due to approximation limitations.

Abstract

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. Models which may lead to a non-viable phenomenology are presented as well in order to understand better the inner framework of this theory. Furthermore, since the velocity of the gravitational waves is set equal to $c_T^2=1$, as stated by the striking event of GW170817 recently, the non-minimal coupling function, the Gauss-Bonnet scalar coupling and the scalar potential are related to each other. Here, we shall assume no particular form of the scalar potential and we choose freely the scalar functions coupled to the Ricci scalar and the Gauss-Bonnet invariant. Certain models are also studied in order to assess the phenomenological validity of the theory, but we need to note that all approximations must hold true in order for a particular model to be valid.