Revisiting Einstein-Gauss-Bonnet Theories after GW170817

TL;DR

This paper explores Einstein-Gauss-Bonnet inflationary models compatible with GW170817 constraints, providing analytic formulas for inflationary parameters and analyzing the coupling function's behavior during reheating.

Contribution

It develops the inflationary formalism for Einstein-Gauss-Bonnet theories under GW170817 constraints and examines the coupling function's evolution during reheating.

Findings

Derived analytic slow-roll indices and observational parameters.

Identified a class of models producing viable inflation.

Analyzed the different behavior of the coupling function during reheating.

Abstract

In this work we study the inflationary framework of Einstein-Gauss-Bonnet theories which produce a primordial gravitational wave speed that respects the constraint imposed by the GW170817 event, namely $\left| c_T^2 - 1 \right| < 6 \times 10^{-15}$ in natural units. For these theories in general, the scalar Gauss-Bonnet coupling function $\xi (\phi)$ is arbitrary and unrelated to the scalar potential. We develop the inflationary formalism of this theory, and present analytic forms for the slow-roll indices, the observational indices and the $e$-foldings number, assuming solely a slow-roll era and also that the constraints imposed by the GW170817 event hold true. We present in detail an interesting class of models that produces a viable inflationary era. Finally, we investigate the behavior of the Einstein-Gauss-Bonnet coupling function during the reheating era, in which case the evolution of the Hubble rate satisfies a constant-roll-like relation $\dot{H}=\delta H^2$. As we show, the behavior of the scalar Gauss-Bonnet coupling during the reheating is different from that of the inflationary era. This is due to the fact that the evolution governing the reheating is different compared to the inflationary era.