Cosmological dynamics of viable f(R) theories of gravity

TL;DR

This paper analyzes the cosmological dynamics of the Hu-Sawicki f(R) gravity model, identifying stable de Sitter points and showing how initial conditions influence the universe's expansion history compared to Lambda CDM.

Contribution

It provides a complete phase-space analysis of the Hu-Sawicki f(R) model for specific parameters and explores how initial conditions affect cosmological evolution.

Findings

Identified stable de Sitter equilibrium points.

Found that standard parameters lead to a non-Lambda CDM expansion history.

Showed that appropriate initial conditions can recover Lambda CDM-like evolution.

Abstract

A complete analysis of the dynamics of the Hu-Sawicki modification to General Relativity is presented. In particular, the full phase-space is given for the case in which the model parameters are taken to be n=1, c1=1, and several stable de Sitter equilibrium points together with an unstable "matter-like" point are identified. We find that if the cosmological parameters are chosen to take on their Lambda CDM values today, this results in a universe which, until very low redshifts, is dominated by an equation of state parameter equal t1/3, leading to an expansion history very different from Lambda CDM. We demonstrate that this problem can be resolved by choosing Lambda CDM initial conditions at high redshifts and integrating the equations to the present day.