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Topology and fragility in cosmology. (English) Zbl 0974.83060
Summary: We introduce the notion of topological fragility and briefly discuss some examples from the literature. An important example of this type of fragility is the way globally anisotropic Bianchi V generalizations of the FLRW \(k=-1\) model result in a radical restriction on the allowed topology of spatial sections, thereby excluding compact cosmological models with negatively curved three-sections with anisotropy. An outcome of this is to exclude chaotic mixing in such models, which may be relevant, given the many recent attempts at employing FLRW \(k=-1\) models to produce chaotic mixing in the cosmic microwave background radiation, if the Universe turns out to be globally anisotropic.

83F05 Relativistic cosmology
83C15 Exact solutions to problems in general relativity and gravitational theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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