Stability and Space Phase Analysis in f(R) theory with Generalized Exponential model

TL;DR

This paper analyzes the stability of dynamical systems in f(R) gravity, focusing on a generalized exponential model and a power-law model, identifying critical points and their stability conditions related to cosmic evolution.

Contribution

It introduces a detailed dynamical analysis of f(R) gravity with a generalized exponential and a new power-law model, highlighting stability conditions dependent on model parameters.

Findings

Identified six critical points in the dynamical system.

Found only one critical point representing a universe with matter and dark energy.

Stability conditions depend on specific model parameters.

Abstract

We have studied in this paper, the stability of dynamical system in $f(R)$ gravity. We have considered the $f(R)$ $\gamma$-gravity and explored its dynamical analysis. We found six critical points among which only one describes an universe fulled of both matter and dominated dark energy. It's shown that these critical points presents specific phase spaces described by the corresponding fluids. Furthermore, we've investigated the stability conditions of these critical points and find that theses conditions are dependent of the model parameters. We also study the stability of a new power-law $f_\ast(R)$ model with de Sitter and power law solutions.