Revisiting Einstein-Gauss-Bonnet Theories after GW170817 (2407.12155v1)

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.