The evolution and diagnosis in late-time F ( R ) dark energy model

We systematically review some standard problems and recent developments in modified gravitation in cosmology, and in this paper study the late -time dynamics of the F ( R ) gravity model. We discuss three important issues, namely the cosmological evolution of the F ( R ) gravity model, statefinder geometric diagnosis, and cosmological implications from supernova observations. We will solve the field equation appropriately by using the state search function. We consider the model, described by a nearly R 2 -model at early epochs, and we fine -tune the parameters to achieve feasibility and compatibility with the latest Planck constraints later on. On this basis, we derive the evolution equations of the density parameters, EoS parameters and deceleration parameters of the model, and find that they can explain the cosmological evolution well. In addition, we discuss the statefinder geometric diagnosis of the model, plotting the evolutionary trajectory of r and s with redshift z and ( r, s ) , ( r, q ) . We found that this model can be clearly distinguished from the ACDM model. Finally, we compare the theoretical model with the cosmological constant model and find that the theoretical results fit SN I a data well.