On inflationary parameters in scalar–tensor theories

Abstract

The equivalence between f (R) and scalar-tensor theories is revisited, we consequently explored different f (R) models. After consideration of specific definition of the scalar field, we derived the potentials V (φ) for each f (R) model focusing on the early Universe, mostly the inflation epoch. For a given potential, we applied the slow-roll approximation approach to each f (R) model and obtained the expressions for the spectral index n s and tensor-to-scalar ratio r. We determined the corresponding numerical values associated with each of the f (R) models. Our results showed that for certain choice of parameter space, the values of n s and r 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 (KGE) of each f (R) model. We found numerical solutions to each KGE considering different values of free parameters and initial conditions of each f (R) 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.