On inflationary parameters in scalar–tensor theories

Abstract

The equivalence between [Formula: see text] and scalar–tensor theories is revisited, we consequently explored different [Formula: see text] models. After consideration of specific definition of the scalar field, we derived the potentials [Formula: see text] for each [Formula: see text] model focusing on the early Universe, mostly the inflation epoch. For a given potential, we applied the slow-roll approximation approach to each [Formula: see text] model and obtained the expressions for the spectral index [Formula: see text] and tensor-to-scalar ratio [Formula: see text]. We determined the corresponding numerical values associated with each of the [Formula: see text] models. Our results showed that for certain choice of parameter space, the values of [Formula: see text] and [Formula: see text] are consistent with the Planck survey results and others produce numerical values that are in the same range as suggested by Planck data. We further constructed the Klein–Gordon equations (KGEs) of each [Formula: see text] model. We found numerical solutions to each KGE considering different values of free parameters and initial conditions of each [Formula: see text] model. All models showed that the scalar field decreases as time increases, an indication that there is less content of the scalar field in the late Universe.