Paths of Friedmann-Robertson-Walker brane models

TL;DR

This paper reviews the dynamics of brane-world dark energy models, showing they can be represented as 2D dynamical systems, and finds that generic models are topologically equivalent to the standard Lambda-CDM cosmology.

Contribution

It introduces a unified dynamical systems framework for brane dark energy models and characterizes their generic behavior using structural stability and Peixoto theorem.

Findings

Generic brane models are topologically equivalent to Lambda-CDM.

Bouncing and transient acceleration models are non-generic.

A single scheme unifies various brane dark energy models.

Abstract

Dynamics of brane-world models of dark energy is reviewed. We demonstrate that simple dark energy brane models can be represented as 2-dimensional dynamical systems of a Newtonian type. Hence a fictitious particle moving in a potential well characterizes the model. We investigate the dynamics of the brane models using methods of dynamical systems. The simple brane-world models can be successfully unified within a single scheme -- an ensemble of brane dark energy models. We characterize generic models of this ensemble as well as exceptional ones using the notion of structural stability (instability). Then due to the Peixoto theorem we can characterize the class of generic brane models. We show that global dynamics of the generic brane models of dark energy is topologically equivalent to the concordance $\Lambda$CDM model. We also demonstrate that the bouncing models or models in which acceleration of the universe is only transient phenomenon are non-generic (or exceptional cases) in the ensemble. We argue that the adequate brane model of dark energy should be a generic case in the ensemble of FRW dynamical systems on the plane.