A dynamical system approach to Bianchi III cosmology for Hu–Sawicki type f(R) gravity

The cosmological dynamics of spatially homogeneous but anisotropic Bianchi type-III space-time is investigated in presence of a perfect fluid within the framework of Hu–Sawicki model. We use the dynamical system approach to perform a detailed analysis of the cosmological behaviour of this model for the model parameters n=1,c1=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1, c_1=1$$\end{document}, determining all the fixed points, their stability and corresponding cosmological evolution. We have found stable fixed points with de Sitter solution along with unstable radiation like fixed points. We have identified a matter like point which act like an unstable spiral and when the initial conditions of a trajectory are very close to this point, it stabilizes at a stable accelerating point. Thus, in this model, the universe can naturally approach to a phase of accelerated expansion following a radiation or a matter dominated phase. It is also found that the isotropisation of this model is affected by the spatial curvature and that all the isotropic fixed points are found to be spatially flat.