Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-09-28
Class.Quant.Grav.22:607-634,2005
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
30 pages, many postscript figures
Scientific paper
10.1088/0264-9381/22/3/010
Using dynamical systems theory and a detailed numerical analysis, the late-time behaviour of tilting perfect fluid Bianchi models of types IV and VII$_h$ are investigated. In particular, vacuum plane-wave spacetimes are studied and the important result that the only future attracting equilibrium points for non-inflationary fluids are the plane-wave solutions in Bianchi type VII$_h$ models is discussed. A tiny region of parameter space (the loophole) in the Bianchi type IV model is shown to contain a closed orbit which is found to act as an attractor (the Mussel attractor). From an extensive numerical analysis it is found that at late times the normalised energy-density tends to zero and the normalised variables 'freeze' into their asymptotic values. A detailed numerical analysis of the type VII$_h$ models then shows that there is an open set of parameter space in which solution curves approach a compact surface that is topologically a torus.
Coley Alan
den Hoogen Robert van
Hervik Sigbjorn
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