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

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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 ( $$\epsilon $$ ϵ ), the tensor-to-scalar ratio ( r ), and the scalar spectral index ( $$n_s$$ n s ) during inflation. We have found $$r=0.0011$$ r = 0.0011 , and $$n_s= 0.9647$$ 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 ( $$0.009983\,\,\textrm{to}\,\, 0.00022$$ 0.009983 to 0.00022 ) and $$n_s$$ n s ( $$0.9597\,\, \textrm{to}\, \, 0.9707$$ 0.9597 to 0.9707 ), which lie well within the Planck-2018 data in 68% and 95% C.L. The non-Gaussian parameters $${f}_{NL}$$ f NL ( $$-0.0167824$$ - 0.0167824 to $$-0.01222$$ - 0.01222 ), $${\tau }_{NL}$$ τ NL ( $$2.816\times 10^{-4}$$ 2.816 × 10 - 4 to $$1.49\times 10^{-4}$$ 1.49 × 10 - 4 ) and $${g}_{NL}

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