Structural stability properties of friedman cosmology

Journal of Mathematical Physics

Hrycyna

2008

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.

Section: Brane Dark Energy Models As a Dynamical Systems Concludmentioning

confidence: 98%

Paths of Friedmann–Robertson–Walker brane models

Journal of Mathematical Physics

Hrycyna

2008

“…2. The physically realistic models of the world should possess some kind of the structural stability because having so many dramatically different models all agreeing with observation would be fatal for the empirical method of science (Shtanov 2000;Sahni 2003, see also Thom 1977;Szydlowski et al 1984;Biesiada 2003;Golda et al 1987;Tavakol and Ellis 1988).…”

Section: Structural Stability Issuesmentioning

confidence: 99%

“…A certain property (such as acceleration, singularities etc.) is believed to be realistic if it can be attributed to a large subset of models within the space of all solutions (Szydlowski et al 1984). The evolutional scenarios are represented by the phase curves or by critical points, limit circles or the other limit sets.…”

Section: Genericity Of Acceleration Scenario In the Framework Of Strumentioning

confidence: 99%

Generic scenarios of the accelerating Universe

2012

Astrophys Space Sci

Recent astronomical observations strongly indicate that the current Universe is undergoing an accelerated phase of its expansion. If the Universe evolution is described by the FRW model then the acceleration should be driven by some perfect substance violating the strong energy condition. Hence the negative pressure is required for the explanation of acceleration. While different candidates for the fluid termed dark energy have been suggested, the positive cosmological constant seems to be the simplest candidate for dark energy description. However the Lambda term treated as a quantum vacuum energy has no simple physical interpretation because of the fine tuning problem. In this paper we characterize a certain class of evolutional scenario of the accelerating universe from the point of view genericity expressed in notion of structural stability. It is shown that in this class all evolutional scenarios with transient acceleration effect are not generic. Only the LCDM model with the acceleration phase following the deceleration phase is structurally stable. Because the cosmological models with transient acceleration appear in string theory we conclude that they are not generic.

“…Such a cosmological model with the imperfect fluid ( D const) has been considered since Heller et al [3] and Belinskii et al [4]. The Einstein field equation (2) for this model reduces to [5] …”

Section: Introductionmentioning

confidence: 99%

Lyapunov function for cosmological dynamical system

Demonstratio Mathematica

Krawiec

2017

Abstract:We prove the asymptotic global stability of the de Sitter solution in the Friedmann-Robertson-Walker conservative and dissipative cosmology. In the proof we construct a Lyapunov function in an exact form and establish its relationship with the first integral of dynamical system determining evolution of the flat Universe. Our result is that de-Sitter solution is asymptotically stable solution for general form of equation of state p D p. ; H /, where dependence on the Hubble function H means that the effect of dissipation are included.