Growth of matter perturbations for realistic $F(R)$ models

TL;DR

This paper investigates the growth of matter perturbations in two realistic $F(R)$ gravity models, developing parametrizations of the growth index to differentiate these models from others using observational data.

Contribution

It introduces specific parametrizations of the growth index for two $F(R)$ models and demonstrates their effectiveness in characterizing and distinguishing these models from alternatives.

Findings

The growth index is best described by $\gamma = \gamma_0 + \gamma_1 z/(1+z)$ for both models.

Values of $\gamma_0$ and $\gamma_1$ effectively characterize the models.

The models are consistent with current observational data.

Abstract

Two different realistic $F(R)$ modified gravity models are considered in the framework of the Friedmann-Lemetre-Robertson-Walker universe. The parameters of these two models are adjusted to reach coherence with the most recent and accurate observations of the current universe. A study of the growth of matter density perturbations is done, and several parametrizations of the growth index are developed for both models. The ansatz for the growth index given by $\gamma = \gamma_0 + \gamma_1 z/(1+z)$ seems to be the best parametrization for the two models considered. Finally, the values obtained for $\gamma_0$ and $\gamma_1$ can be used in order to characterize these two models and to differentiate them from others such as the Hu-Sawicki model.