Paths of Friedmann–Robertson–Walker brane models

Abstract

The dynamics of brane-world models of dark energy is reviewed. We demonstrate that simple dark energy brane models can be represented as two-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 the global dynamics of the generic brane models of dark energy is topologically equivalent to the concordance ΛCDM model. We also demonstrate that the bouncing models or models in which acceleration of the universe is only transient phenomenon are nongeneric (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 Friedmann–Robertson–Walker dynamical systems on the plane.