Paths of Friedmann–Robertson–Walker brane 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 ΛCDM 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.

Classification of the FRW universe with a cosmological constant and a perfect fluid of the equation of state p = w ρ

“…Similar considerations were also carried out in a series of papers, and particular attention was paid to obtaining an effective potential V (a) by fitting observational data sets [43][44][45][46][47][48]. In this paper, we shall not consider the fitting of these models, but simply provide a complete classification of all such models.…”

“…The main idea is simply to cast the dynamical equation in the form of the conservation of total energy of a classical particle with mass m moving under the influence of a potential V (x) [42][43][44][45][46][47][48],…”

Thermodynamics and classification of cosmological models in the Horava-Lifshitz theory of gravity

“…Without loss of generality, we can always set a 0 = 1. Then, it can be shown that the Friedmann equation (3.3) can be cast in the form [17,18], 1 2 a * 2 + V (a) = 0, (5.3) where a * ≡ da(t)/d(H 0 t), and…”

“…It should be noted that classification of a (nonrelativistic) matter coupled with a dark energy was considered recently in [16], in the framework of Einstein's theory, and the corresponding Penrose diagrams were presented. Similar considerations were also carried out in a series of papers, and particular attention was paid to obtain an effective potential V (a) by fitting observational data sets [17]. In [18], such studies were generalized to a perfect fluid with the equation of state p = wρ.…”