Topology and Fragility in Cosmology

TL;DR

This paper introduces the concept of topological fragility in cosmology, illustrating how anisotropy can restrict the topology of spatial sections and impact phenomena like chaotic mixing in the universe.

Contribution

It defines topological fragility and explores its implications for the topology of anisotropic cosmological models, especially Bianchi V and FLRW models.

Findings

Anisotropy restricts the topology of spatial sections.

Certain models exclude compact negatively curved topologies.

Implications for chaotic mixing in the cosmic microwave background.

Abstract

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 generalisations 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 compact FLRW $k=-1$ models to produce chaotic mixing in the cosmic microwave background radiation, if the Universe turns out to be globally anisotropic.