Bianchi VIII and IX vacuum cosmologies: Almost every solution forms particle horizons and converges to the Mixmaster attractor

Bernhard Brehm

Bianchi VIII and IX vacuum cosmologies: Almost every solution forms particle horizons and converges to the Mixmaster attractor

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arxiv 1606.08058 v1 pith:2JKJPYLA submitted 2016-06-26 gr-qc

Bianchi VIII and IX vacuum cosmologies: Almost every solution forms particle horizons and converges to the Mixmaster attractor

Bernhard Brehm This is my paper

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keywords bianchivacuumviiitowardsalmostattractoreverygeneric

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Bianchi models are posited by the BKL picture to be essential building blocks towards an understanding of generic cosmological singularities. We study the behaviour of spatially homogeneous anisotropic vacuum spacetimes of Bianchi type VIII and IX, as they approach the big bang singularity. It is known since 2001 that generic Bianchi IX spacetimes converge towards the so-called Mixmaster attractor as time goes towards the singularity. We extend this result to the case of Bianchi VIII vacuum. The BKL picture suggests that particle horizons should form, i.e. spatially separate regions should causally decouple. We prove that this decoupling indeed occurs, for Lebesgue almost every Bianchi VIII and IX vacuum spacetime.

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