Viable inflation in scalar-Gauss-Bonnet gravity and reconstruction from observational indices

In this paper we on inflationary dynamics in the context of Einstein-Gauss-Bonnet gravitational theories. We investigate the implications of the slow-roll condition on the slow-roll indices and we investigate how the inflationary dynamical evolution is affected by the presence of the Gauss-Bonnet coupling to the scalar field. To exemplify our analysis, we investigate how the dynamics of inflationary cubic-order, quartic-order, and exponential scalar potentials are affected by the nontrivial Gauss-Bonnet coupling to the scalar field. As we demonstrate, it is possible to obtain a viable phenomenology compatible with the observational data, although the canonical scalar field theory with cubic- and quartic-order potentials does not yield phenomenologically acceptable results. In addition, with regard to the exponential potential example, the Einstein-Gauss-Bonnet extension of the single canonical scalar field model has an inherent mechanism that can trigger the graceful exit from inflation. Furthermore, we introduce a bottom-up reconstruction technique where, by fixing the tensor-to-scalar ratio and the Hubble rate as a function of the e-folding number, one is capable of reproducing the Einstein-Gauss-Bonnet theory which generates the aforementioned quantities. We illustrate how the method works by using some relatively simple examples.