Study of early inflationary phase with minimal and non-minimal coupling using string-motivated potential

Abstract

We study the early inflationary phase using a potential derived from type IIB/F theory within the frameworks of minimally and non-minimally coupled scalar fields to gravity. The well-known cosmological Klein–Gordon equation based on a single scalar field with a stringy potential is solved numerically for both setups. The solutions obtained are consistent with the Friedmann equation. We first use a solution for minimal setup to calculate some important inflationary parameters, e.g., first slow-roll parameter (\(\epsilon \)), the tensor-to-scalar ratio (r), and the scalar spectral index (\(n_s\)) during inflation. We have found \(r=0.0011\), and \(n_s= 0.9647\), that lie well inside the Planck-2018 data. Specifically, we investigate a solution for a non-minimal setup to explore the non-Gaussianity. In this scenario, a conformal transformation is used to study the various inflationary parameters in the Jordan- and Einstein frames. We have calculated the potential slow-roll parameters predicting the range for r (\(0.009983\,\,\textrm{to}\,\, 0.00022\)) and \(n_s\) (\(0.9597\,\, \textrm{to}\, \, 0.9707\)), which lie well within the Planck-2018 data in 68% and 95% C.L. The non-Gaussian parameters \({f}_{NL}\) (\(-0.0167824\) to \(-0.01222\)), \({\tau }_{NL}\) (\(2.816\times 10^{-4}\) to \(1.49\times 10^{-4}\)) and \({g}_{NL}\) (\(-2.877\times 10^{-4}\) to \(-1.673\times 10^{-4}\)) for non-minimal coupling constant \(\xi \) ranging from 0.001 to 0.0001 with 60 e-folds are obtained. We have elucidated the graceful exit phenomenon from the inflationary phase for both setups. The application of the technique of dynamical systems analysis offers insights into the stability and the dynamic nature of the inflationary solution in the phase space, that indicates the starting and ending of the inflationary period.