On a proof of the collapse conjecture for a diagonal Bianchi type-IX vacuum space-time

TL;DR

This paper provides a straightforward proof of the collapse conjecture for diagonal Bianchi type-IX vacuum space-times, demonstrating that the universe cannot escape to infinity along anisotropic channels.

Contribution

It introduces a simple proof showing the impossibility of escape along channels in the anisotropy plane for this cosmological model.

Findings

The stable attractor at infinity has non-zero codimension.

Escape along channels in the anisotropy plane is impossible.

The proof simplifies previous approaches to the collapse conjecture.

Abstract

It is given a simple proof of the collapse conjecture for a diagonal Bianchi type-IX vacuum space-time. It is shown that the codimension of the infinity stable attractor, restricted to the anisotropy plane, is not zero, thus proving that "escape along a channel" is impossible.