Chaotic scalar fields as models for dark energy

Beck, Christian

doi:10.1103/physrevd.69.123515

Cited by 32 publications

(53 citation statements)

References 52 publications

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“…This author, suggested that the dynamical behavior of this nonintegrable model is similar to the chaos appearing in ergodic systems. Since then, the problem of chaos in FRW scalar field cosmologies has been investigated thoroughly in several papers [10,12,13,14,15,16,17,18,19,20,21]. The dynamical properties of such cosmological models are met in dynamical systems exhibiting chaotic scattering.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and chaos in the unified scalar field cosmology

2008

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We study the dynamics of the closed scalar field FRW cosmological models in the framework of the so called Unified Dark Matter (UDM) scenario. Performing a theoretical as well as a numerical analysis we find that there is a strong indication of chaos in agreement with previous studies. We find that a positive value of the spatial curvature is essential for the appearance of chaoticity, though the Lyapunov number seems to be independent of the curvature value. Models that are close to flat (k → 0 + ) exhibit a chaotic behavior after a long time while pure flat models do not exhibit any chaos. Moreover, we find that some of the semiflat models in the UDM scenario exhibit similar dynamical behavior with the Λ cosmology despite their chaoticity.Finally, we compare the measured evolution of the Hubble parameter derived from the differential ages of passively evolving galaxies with that expected in the semiflat unified scalar field cosmology. Based on a specific set of initial conditions we find that the UDM scalar field model matches well the observational data.

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Section: Introductionmentioning

confidence: 99%

Dynamics and chaos in the unified scalar field cosmology

2008

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“…For example, it has been shown that these types of non-hyperbolic CMLs naturally arise from stochastically quantised scalar field theories in the anti-integrable limit [4]. They can serve as useful models for vacuum fluctuations and dark energy in the universe [15]. Other applications include chemical kinetics as described by discretised reaction diffusion dynamics [3].…”

Section: Introductionmentioning

confidence: 99%

Scaling behavior of nonhyperbolic coupled map lattices

Groote

Beck

2006

Phys. Rev. E

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Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical systems we study diffusively coupled Tchebyscheff maps of N -th order which exhibit strongest possible chaotic behaviour for small coupling constants a. We prove that the expectations of arbitrary observables scale with √ a in the low-coupling limit, contrasting the hyperbolic case which is known to scale with a. Moreover we prove that there are log-periodic oscillations of period log N 2 modulating the √ a-dependence of a given expectation value. We develop a general 1st order perturbation theory to analytically calculate the invariant 1-point density, show that the density exhibits log-periodic oscillations in phase space, and obtain excellent agreement with numerical results.

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“…The remarkable observation, however, is that these types of coupled map lattices seem to distinguish certain numerical values of coupling constants that coincide with those observed in the standard model of electroweak and strong interaction. For more details on this, see [5,24,25,26,27,28]. The main idea underlying this approach is that indeed the fundamental constants of nature may be fixed by dynamically evolving chaotic states of vacuum fluctuations that possess the strongest random properties that are possible for a smooth coupled deterministic chaotic system.…”

Section: Introductionmentioning

confidence: 99%

Discrete symmetries of chaotic strings

Schäfer

Beck

2010

Dynamical Systems

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Chaotic strings are particular classes of coupled map lattices that can serve as models for vacuum fluctuations in stochastically quantized field theories. They have been previously shown to distinguish standard model coupling parameters as corresponding to states of strongest possible chaotic behaviour and vanishing nearest-neighbour correlation. In this paper we look at discrete symmetry transformations for chaotic strings. We show that several of the chaotic string dynamics can be transformed into each other by simple discrete coordinate transformations. We investigate how expectation values converge in the various coupling parameter regions and single out those stable zeros of the correlation function that correspond to ergodic states with well-defined convergence properties.

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Chaotic scalar fields as models for dark energy

Cited by 32 publications

References 52 publications

Dynamics and chaos in the unified scalar field cosmology

Dynamics and chaos in the unified scalar field cosmology

Scaling behavior of nonhyperbolic coupled map lattices

Discrete symmetries of chaotic strings

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