A class of simple bouncing and late-time accelerating cosmologies in gravity.

We consider the field equations for a flat FRW cosmological model, given by Eq. (??), in an a priori generic gravity model and cast them into a, completely normalized and dimensionless, system of ODEs for the scale factor and the function , with respect to the scalar curvature . It is shown that under reasonable assumptions, namely for power-law functional form for the 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 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 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. [ABSTRACT FROM AUTHOR]