An intermediate inflation of the early Universe from f(R) gravity

Abstract

In this work, we study on the inflationary era of the Universe in the context of f(R) gravity. For this purpose, we consider the f(R) gravity and its scalar perturbation equations. We start with an equation symmetry approach, a notation, which characterizes both the field equations of the gravity and evolution of the scalar perturbations. Throughout the study, to realize inflation we assume that the first slow-roll parameter $$\epsilon _{1}$$ takes a small value with the number of e-folds which has nearly a constant value as $$N\sim 60$$ . An intermediate inflation, which has an initial condition (the Bunch–Davies vacuum state), is obtained. Here, the resulting solution eventually causes the universe enters to the radiation era. Viability of this inflation scenario is investigated by calculating the power spectrum of the primordial curvature perturbations which is observed nearly scale-invariant with some parameters of the intermediate scale factor. Then, the two observable parameters (i.e., the scalar spectral index parameter and the tensor-to-scalar ratio) are obtained. The findings are compared with latest observational data, and we have observed that this inflation scenario for the early universe is possible.