Bianchi I and V cosmologies with Hu-Sawicki f(R) gravity in Palatini formalism

Abstract

The main objective of this work is the pursuit of a detailed analysis of the cosmological solutions corresponding to each fixed point belonging to an exclusive form of f(R) initially introduced by Hu and Sawicki in the background of Palatini f(R) gravity. Fixed points and their associated solutions for the anisotropic Bianchi type I and V models are derived by utilizing an approach used to solve autonomous ordinary differential equations. Building on this background, an exhaustive study on the phase space is accomplished and the existence of a sequence of evolution that starts from unstable anisotropic universe to a stable phase of late times de Sitter expansion through the standard radiation and matter dominated era has been established.