Stability analysis for cosmological models in $f(R)$ gravity using dynamical system analysis

Abstract

Modified gravity theories have received increased attention lately to understand the late time acceleration of the universe. This viewpoint essentially modifies the geometric components of the universe. Among numerous extension to Einstein's theory of gravity, theories which include higher order curvature invariant, and specifically the class of $f(R)$ theories, have received several acknowledgments. In our current work we try to understand the late time acceleration of the universe by modifying the geometry of the space and using dynamical system analysis. The use of this technique allows to understand the behavior of the universe under several circumstances. Apart from that we study the stability properties of the critical point and acceleration phase of the universe which could then be analyzed with observational data. We consider a particular model $f(R)=R-\mu R_c(R/R_c{)}^p$ with $0<p<1,\mu ,R_c>0$ for the study. As a first case we consider the matter and radiation component of the universe with an assumption of no interaction between them. Later, as a second case we take matter, radiation and dark energy (cosmological constant) where study on effects of linear, non-linear and no interaction between matter and dark energy is considered and results have been discussed in detail.

16 pages and 10 figures, published in EPJ C

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• Teleparallel Gravity: From Theory to Cosmology
• Anisotropic compact stars in $f(R)$ gravity
• Validation of Energy Conditions in Wormhole Geometry within Viable $f(R)$ Gravity
• Dynamical system analysis of generalized energy-momentum-squared gravity
• Traversable wormholes in $f(R)$ gravity with constant and variable redshift functions
• Non-trivial black hole solutions in $f(R)$ gravitational theory
• FRW Cosmology in $f(Q,T)$ Gravity
• Static Traversable Wormholes in $f(R,T)=R+2\alpha \ln T$ Gravity
• Anisotropic compact stars in higher-order curvature theory
• Reconstruction and Stability Analysis of Some Cosmological Bouncing Solutions in $F(\mathcal{R},T)$ Theory
• Observational constrained $F(R,\mathcal{G})$ gravity cosmological model and the dynamical system analysis
• Estimation of Cosmological Parameters, Stability Analysis and Energy Conditions in Viable Modified Gravity
• Stability analysis of f(Q) gravity models using dynamical systems
• New rotating AdS/dS black holes in $\mathrm{f}(\mathrm{R})$ gravity
• Cosmological model with time varying deceleration parameter in $F(R,G)$ gravity
• Accelerating Cosmological Models in $f(T,B)$ Gravitational Theory
• A Non-static Quantum inspired Spacetime in $f(R)$ Gravity: Gravity's Rainbow
• Wormhole modeling in $R^2$ gravity with linear trace term
• Cosmological dynamics of f(R) models in dynamical system analysis
• A generic dynamical system formulation for Bianchi-I cosmology with isotropic fluid in $f(Q)$ gravity
• Constructing Viable Interacting Dark Matter and Dark Energy Models: A Dynamical Systems Approach
• An innovative black hole solution and thermodynamic properties in higher-order curvature gravity with a scalar field
• Qualitative behaviour of higher-curvature gravity with boundary terms i.e the f(Q) gravity models by dynamical system analysis
• Generic autonomous system approach to interacting dark energy models
• Late-Time Cosmic Acceleration in Ricci-Gauss-Bonnet Gravity via Gradient Descent Optimization