J Wainwright et al 1999 Class. Quantum Grav. 16 2577 doi:10.1088/0264-9381/16/8/302
Asymptotic self-similarity breaking at late times in cosmology
J Wainwright
, M J Hancock and C Uggla
We study the late-time evolution of a class of exact anisotropic cosmological solutions of Einstein's equations, namely spatially homogeneous cosmologies of Bianchi type VII0 with a perfect fluid source. We show that, in contrast to models of Bianchi type VIIh which are asymptotically self-similar at late times, Bianchi VII0 models undergo a complicated type of self-similarity breaking. This symmetry breaking affects the late-time isotropization that occurs in these models in a significant way: if the equation of state parameter 
satisfies 
(4/3) the models isotropize as regards the shear but not as regards the Weyl curvature. Indeed, these models exhibit a new dynamical feature that we refer to as Weyl curvature dominance: the Weyl curvature dominates the dynamics at late times. By viewing the evolution from a dynamical systems perspective we show that, despite the special nature of the class of models under consideration, this behaviour has implications for more general models.
- PACS
- MSC
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83C20 Classes of solutions; algebraically special solutions, metrics with symmetries
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)
- Subjects
- Dates
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Issue 8 (August 1999)
Received 4 December 1998
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Asymptotic self-similarity breaking at late times in cosmology
J Wainwright et al 1999 Class. Quantum Grav. 16 2577
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Comments on closed Bianchi models
Y Fujiwara et al 1993 Class. Quantum Grav. 10 859
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Clifform calculus with applications to classical field theories
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G Ehlers et al 2003 J. Phys.: Condens. Matter 15 L9
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Nano-displacement measurements using spatially multimode squeezed light
N Treps et al 2004 J. Opt. B: Quantum Semiclass. Opt. 6 S664
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Generation of a phase-flipped Gaussian mode for optical measurements
V Delaubert et al 2002 J. Opt. A: Pure Appl. Opt. 4 393
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