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

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.

16 pages and 6 figures, version accepted for publication in IJMPD

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• Dynamical Systems Perspective of Cosmological Finite-time Singularities in $f(R)$ Gravity and Interacting Multifluid Cosmology
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• Effects of Spatial Curvature on the $f(R)$ Gravity Phase Space: no Inflationary Attractor?
• Autonomous Dynamical System Approach for Inflationary Gauss-Bonnet Modified Gravity
• A Study of Finite-time Singularities of Loop Quantum Cosmology Interacting Multifluids
• Autonomous Dynamical System of Einstein-Gauss-Bonnet Cosmologies
• The Classical and Loop Quantum Cosmology Phase Space of Interacting Dark Energy and Superfluid Dark Matter
• Autonomous Dynamical System Description of de Sitter Evolution in Scalar Assisted $f(R)-\varphi$ Gravity
• The Phase Space of $k$-Essence $f(R)$ Gravity Theory
• Generalized Logarithmic Equation of State in Classical and Loop Quantum Cosmology Dark Energy-Dark Matter Coupled Systems
• Phase Space description of Nonlocal Teleparallel Gravity