Inflation constraints for classes of f(R) models.

In this paper, we explore the equivalence between two theories, namely f (R) and scalar–tensor theories of gravity. We use this equivalence to explore several f (R) toy models focusing on the inflation epoch of the early universe. The study is done based on the definition of the scalar field in terms of the first derivative of f (R) model. We have applied the slow-roll approximations during inflationary parameters consideration. The comparison of the numerically computed inflationary parameters with the observations is done. We have inspected that some of the f (R) models produce numerical values of n s that are in the same range as the suggested values from observations. But for the case of the tensor-to-scalar ratio r , we realized that some of the considered f (R) models suffer to produce a value which is in agreement with the observed values for different considered space parameter. [ABSTRACT FROM AUTHOR]