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.
