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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.

MSC:
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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