Cosmological dynamical systems in modified gravity

TL;DR

This paper presents a model-independent dynamical systems approach to analyze homogeneous and isotropic cosmological models in various modified gravity theories, enabling generic insights before model-specific details are considered.

Contribution

It introduces a universal method using standard cosmological density parameters to study modified gravity models as autonomous dynamical systems, despite more complex constraints.

Findings

Applicable to many modified gravity models

Extracts generic dynamical behavior

Facilitates comparison across models

Abstract

The field equations of modified gravity theories, when considering a homogeneous and isotropic cosmological model, always become autonomous differential equations. This relies on the fact that in such models all variables only depend on cosmological time, or another suitably chosen time parameter. Consequently, the field equations can always be cast into the form of a dynamical system, a successful approach to study such models. We propose a perspective that is applicable to many different modified gravity models and relies on the standard cosmological density parameters only, making our choice of variables model independent. The drawback of our approach is a more complicated constraint equation. We demonstrate our procedure studying various modified gravity models and show how much generic information can be extracted before a specific model is considered.