Viable Inflation in Scalar-Gauss-Bonnet Gravity and Reconstruction from Observational Indices

TL;DR

This paper explores inflationary models within Einstein Gauss-Bonnet gravity, demonstrating how non-trivial couplings can produce viable inflationary scenarios compatible with observations and introducing a reconstruction method based on observational indices.

Contribution

It analyzes the impact of Gauss-Bonnet coupling on inflationary dynamics and proposes a bottom-up reconstruction technique for Einstein Gauss-Bonnet theories from observational data.

Findings

Viable inflationary models can be achieved with non-trivial Gauss-Bonnet couplings.

Canonical scalar fields with cubic and quartic potentials are not phenomenologically acceptable.

The exponential potential model can naturally exit inflation due to Gauss-Bonnet effects.

Abstract

In this paper the focus is 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. For exemplification of our analysis we investigate how the dynamics of inflationary cubic, quartic order and also exponential scalar potentials are affected by the non-trivial 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, in the context of which by fixing the tensor-to-scalar ratio and the Hubble rate as a function of the $e$-foldings 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.