Axially symmetric Bianchi I Yang - Mills cosmology as a dynamical system

Darian, Bahman; Künzle, H. P.

doi:10.1088/0264-9381/13/10/005

Cited by 19 publications

(25 citation statements)

References 18 publications

(29 reference statements)

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“…A Axi-symmetric gauge fields A.1 Symmetry constraints Using symmetry, we can make a reduction of variables [44]. In the present system, there are spacetime isometry and gauge symmetry.…”

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confidence: 99%

Anisotropic inflation with non-abelian gauge kinetic function

Murata

Soda

2011

J. Cosmol. Astropart. Phys.

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We study an anisotropic inflation model with a gauge kinetic function for a nonabelian gauge field. We find that, in contrast to abelian models, the anisotropy can be either a prolate or an oblate type, which could lead to a different prediction from abelian models for the statistical anisotropy in the power spectrum of cosmological fluctuations. During a reheating phase, we find chaotic behaviour of the non-abelian gauge field which is caused by the nonlinear self-coupling of the gauge field. We compute a Lyapunov exponent of the chaos which turns out to be uncorrelated with the anisotropy.

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“…A Axi-symmetric gauge fields A.1 Symmetry constraints Using symmetry, we can make a reduction of variables [44]. In the present system, there are spacetime isometry and gauge symmetry.…”

mentioning

confidence: 99%

Anisotropic inflation with non-abelian gauge kinetic function

Murata

Soda

2011

J. Cosmol. Astropart. Phys.

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“…This imposes special symmetries on the dynamics and the dynamical system is integrable: chaos cannot exist [5]. Recently, a Yang-Mills theory was formulated in an axisymmetric, spatially homogeneous universe [6]. The large number of degrees of freedom made an analysis of the full dynamics difficult, and the coordinate dependence of the standard chaotic indicators meant that the relativistic chaos could not be invariantly characterised.In this letter, we analyse general relativistic Yang-Mills chaos using invariant topological methods.…”

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confidence: 99%

“…After fixing the internal gauge of the Yang-Mills field, the matter can be parametrized by two variables (α, γ) [6], which can be thought of as color degrees of freedom for the massless gauge fields. The cosmological evolution is an orbit in the (b, c, α, γ) phase space.…”

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confidence: 99%

Chaos in the Einstein-Yang-Mills Equations

Barrow

Levin

1998

Phys. Rev. Lett.

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Yang-Mills color fields evolve chaotically in an anisotropically expanding universe. The chaotic behaviour differs from that found in anisotropic Mixmaster universes. The universe isotropizes at late times, approaching the mean expansion rate of a radiation-dominated universe. However, small chaotic oscillations of the shear and color stresses continue indefinitely. An invariant, coordinate-independent characterisation of the chaos is provided by means of fractal basin boundaries. CfPA-97-TH-06Yang-Mills fields are central to quantum theories of elementary particles. They are of interest to dynamicists since they evolve chaotically in flat spacetime [1,2,3,4]. But how do Yang-Mills fields behave in the early universe? Does the chaos persist, or is it eradicated by the general relativistic effects of cosmological expansion? The earliest studies of the Einstein-Yang-Mills (EYM) system assumed isotropic cosmological expansion. This imposes special symmetries on the dynamics and the dynamical system is integrable: chaos cannot exist [5]. Recently, a Yang-Mills theory was formulated in an axisymmetric, spatially homogeneous universe [6]. The large number of degrees of freedom made an analysis of the full dynamics difficult, and the coordinate dependence of the standard chaotic indicators meant that the relativistic chaos could not be invariantly characterised.In this letter, we analyse general relativistic Yang-Mills chaos using invariant topological methods. We make the problem more tractable by an economical definition of variables, which reduces the dimension of the phase space substantially (from 8 − D to 5 − D). In the physical picture that emerges, the asymptotic evolution of the spatial volume of the universe imitates a radiation-dominated universe, while the shear diminishes chaotically.Previous studies of chaos in general relativity have focused on the non-axisymmetric Bianchi type VIII and IX (Mixmaster) universes, where the presence of anisotropic 3-curvature creates an infinite sequence of chaotic oscillations on approach to an initial Weyl curvature singularity at t = 0 [12,13,14]. This behaviour is intrinsically general relativistic. By contrast, the chaotic EYM cosmology that we study is different: chaos exists even when the metric is axisymmetric and the curvature is isotropic.We evolve the Yang-Mills fields in the simplest anisotropic metrics of Bianchi type I. The color degrees of freedom of the Yang-Mills gauge fields oscillate chaotically, while the expansion attenuates their overall energy. The EYM action iswhere F µν is the gauge-invariant field strength. The spacetime is described by the axisymmetric Bianchi I metric, with scale factors b(t) and c(t):

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“…In Figure 9, we have represented the potential V associated to the results in Figures 5,6,7,8,11 and 15. The oscillation has been unfolded along the σ−axis and the resulting plot has been split in two for sake of readiness.…”

Section: Discussionmentioning

confidence: 99%

Gravitational instability of Yang–Mills cosmologies

Füzfa¹

2003

Class. Quantum Grav.

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The gravitational instability of Yang-Mills cosmologies is numerically studied with the hamiltonian formulation of the spherically symmetric Einstein-Yang-Mills equations with SU (2) gauge group. On the short term, the expansion dilutes the energy densities of the Yang-Mills fluctuations due to their conformal invariance. In this early regime, the gauge potentials appear oscillating quietly in an interaction potential quite similar to the one of the homogeneous case. However, on the long term, the expansion finally becomes significantly inhomogeneous and no more mimics a conformal transformation of the metric. Thereafter, the Yang-Mills fluctuations enter a complex non-linear regime, accompanied by diffusion, while their associated energy contrasts grow.

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Axially symmetric Bianchi I Yang - Mills cosmology as a dynamical system

Cited by 19 publications

References 18 publications

Anisotropic inflation with non-abelian gauge kinetic function

Anisotropic inflation with non-abelian gauge kinetic function

Chaos in the Einstein-Yang-Mills Equations

Gravitational instability of Yang–Mills cosmologies

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