Inflation constraints for classes of f(R) models

In this paper, we explore the equivalence between two theories, namely f® and scalar-tensor theories of gravity. We use this equivalence to explore several f® 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® 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® 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® models suffer to produce a value which is in agreement with the observed values for different considered space parameter.