Inflation constraints for classes of f(R) models

TL;DR

This paper investigates f(R) gravity models' inflationary predictions, comparing their scalar spectral index and tensor-to-scalar ratio with observations, highlighting which models align with empirical data.

Contribution

It demonstrates the inflationary behavior of various f(R) models using scalar-tensor equivalence and slow-roll approximations, providing a comparison with observational constraints.

Findings

Some f(R) models produce $n_s$ values consistent with observations.

Certain models fail to match the observed tensor-to-scalar ratio $r$.

The study identifies models compatible with current inflationary data.

Abstract

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.