A note on the dynamical system formulations in $f(R)$ gravity

Abstract

A number of dynamical system formulations have been proposed over the last few years to analyse cosmological solutions in f (R) gravity. The aim of this article is to provide a brief introduction to the different approaches, presenting them in a chronological order as they appeared in the history of the relevant scientific literature. In this way we illuminate how the shortcoming(s) of an existing formulation encouraged the development of an alternative formulation. Whenever possible, a 2-dimensional phase portrait is given for a better visual representation of the dynamics of phase space. We also touch upon how cosmological perturbations can be analyzed using the phase space language.

Cosmological dynamical systems in modified gravity

“…This leads to a neat set of equations, but can also introduce problems when f (1) vanishes dynamically during the cosmological evolution, the constraint equation again takes a rather simple form. The mentioned problem has motivated the introduction of other variables which remain regular during the cosmological evolution, see in particular [37,38] where specific f (R) gravity models were studied, see also [39][40][41]. Often, these improved variables lead to more complicated constraint equations.…”