Cosmological dynamics of f(R) models in dynamical system analysis

TL;DR

This paper investigates the late-time acceleration of the universe using dynamical system analysis on specific f(R) gravity models, examining stability and critical points without solving field equations analytically.

Contribution

It introduces a dynamical system approach to analyze the stability of f(R) models' critical points, providing insights into cosmic acceleration behavior.

Findings

Identified stable critical points corresponding to accelerated expansion.

Analyzed the impact of model parameters on stability and cosmic evolution.

Compared theoretical results with observational constraints.

Abstract

In this work we try to understand the late time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe without analytically solving the field equations. We study the acceleration phase of the universe and stability properties of the critical points which could be compared with observational results. We consider an asymptotic behavior of two particular models $f(R) = R - \mu R_{c} \frac{(R/R_c)^{2n}}{(R/R_c)^{2n} + 1}$ and $f(R) = R - \mu R_{c} \left[ 1 - (1 + R^2/R_{c}^2)^{-n} \right]$ with $n,\mu, R_c >0$ for the study. As a first case we fix the value of $\mu$ and analyzed for all $n$. Later as second case, we fix the value of $n$ and calculation are done for all $\mu$. At the end all the calculations for the generalized case have been shown and results have been discussed in detail.