The late-time dynamics of F(R) gravity dark energy model

In this work we shall study the late-time dynamics of F(R) gravity model. We address two important issues, they are respectively the cosmological evolution of F(R) gravity model and the cosmological implication from supernovae observations. We shall solve numerically the field equations by appropriately expressing it in terms of a statefinder function. The F(R) gravity model we considered is described by a nearly R2-model at early epochs, which dominates the evolution during the early time, thus producing a viable inflationary phenomenology. By computation we find that the model predict a phantom evolution. And we fine-tune the parameters to arrive at physically viable cosmology at late times. It is worth noting that dark energy oscillations exist in the model. We find it is possible to realize phantom, nearly de-Sitter and quintessential dark energy eras with simple F(R) gravity models, without resorting to phantom scalar fields or relativistic fluids of any sort. Then we consider the SN Ia observational data, and compared the theoretical results with cosmological constant model (ΛCDM model) and these data through the χ2 statistical test. And as we can see, the theoretical results agree well with SN Ia data.