A new proof of the Bianchi type IX attractor theorem

TL;DR

This paper presents a concise, self-contained new proof of the Bianchi type IX attractor theorem, highlighting the unique nature of type IX models and their asymptotic behavior near singularities.

Contribution

A novel, streamlined proof of the Bianchi type IX attractor theorem that clarifies the special role of type IX models in cosmological dynamics.

Findings

Type IX solutions are governed by Bianchi I and II vacuum states near singularities

The proof emphasizes the unique properties of type IX models

Type IX is somewhat misleading in broader generic models without symmetries

Abstract

We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The `Bianchi type IX attractor theorem' states that the past asymptotic behavior of generic type IX solutions is governed by Bianchi type I and II vacuum states (Mixmaster attractor). We give a comparatively short and self-contained new proof of this theorem. The proof we give is interesting in itself, but more importantly it illustrates and emphasizes that type IX is special, and to some extent misleading when one considers the broader context of generic models without symmetries.