A Study of an Einstein Gauss-Bonnet Quintessential Inflationary Model

In this paper we study a class of quintessential Einstein Gauss-Bonnet models, focusing on their early and late-time phenomenology. With regard to the early-time phenomenology, we formalize the slow-roll evolution of these models and we calculate in detail the spectral index of the primordial curvature perturbations and the tensor-to-scalar ratio. As we demonstrate, the resulting observational indices can be compatible with both the Planck and the BICEP2/Keck-Array observational constraints on inflation. With regard to the late-time behavior, by performing a numerical analysis we demonstrate that the class of models for which the coupling function $\xi (\phi)$ to the Gauss-Bonnet scalar satisfies $\xi (\phi)\sim \frac{1}{V(\phi )}$, produce a similar pattern of evolution, which at late-times is characterized by a decelerating era until some critical redshift, at which point the Universe super-decelerates and subsequently accelerates until present time, with a decreasing rate though. The critical redshift crucially depends on the initial conditions chosen for the scalar field and for all the quintessential Einstein Gauss-Bonnet models studied, the late-time era is realized for large values of the scalar field.