On f(R) gravity in scalar–tensor theories

Abstract

We study [Formula: see text] gravity models in the language of scalar–tensor (ST) theories. The correspondence between [Formula: see text] gravity and ST theories is revisited since [Formula: see text] gravity is a subclass of Brans–Dicke models, with a vanishing coupling constant ([Formula: see text]). In this treatment, four [Formula: see text] toy models are used to analyze the early-universe cosmology, when the scalar field [Formula: see text] dominates over standard matter. We have obtained solutions to the Klein–Gordon equation for those models. It is found that for the first model [Formula: see text], as time increases the scalar field decreases and decays asymptotically. For the second model [Formula: see text], it was found that the function [Formula: see text] crosses the [Formula: see text]-axis at different values for different values of [Formula: see text]. For the third model [Formula: see text], when the value of [Formula: see text] is small, the potential [Formula: see text] behaves like the standard inflationary potential. For the fourth model [Formula: see text], we show that there is a transition between [Formula: see text]. The behavior of the potentials with [Formula: see text] is totally different from those with [Formula: see text]. The slow-roll approximation is applied to each of the four [Formula: see text] models and we obtain the respective expressions for the spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text].