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.