A class of simple bouncing and late-time accelerating cosmologies in f(R) gravity

Abstract

We consider the field equations for a flat FRW cosmological model, given by Eq. (??), in an a priori generic [Formula: see text] gravity model and cast them into a, completely normalized and dimensionless, system of ODEs for the scale factor and the function [Formula: see text], with respect to the scalar curvature [Formula: see text]. It is shown that under reasonable assumptions, namely for power-law functional form for the [Formula: see text] gravity model, one can produce simple analytical and numerical solutions describing bouncing cosmological models where in addition there are late-time accelerating. The power-law form for the [Formula: see text] gravity model is typically considered in the literature as the most concrete, reasonable, practical and viable assumption [see S. D. Odintsov and V. K. Oikonomou, Phys. Rev. D 90 (2014) 124083, arXiv:1410.8183 [gr-qc]]. However even without assuming a power-law form for the [Formula: see text] gravity model, the formulation of the field equations, that is suggested in this paper, is according to the author’s viewpoint quite generic in order to analyze the resulting field equations, without any further assumptions. Possibility of extending these results is briefly discussed.