Comparing the dynamics of diagonal and general Bianchi IX spacetime

TL;DR

This paper compares the dynamics of diagonal and nondiagonal Bianchi IX cosmological models near singularities, revealing higher-dimensional nonhyperbolic critical spaces and suggesting potential new chaos types in the nondiagonal case.

Contribution

It provides a detailed dynamical systems analysis of both models, highlighting differences in critical space topology and proposing new chaos phenomena in nondiagonal Bianchi IX.

Findings

Critical spaces are higher dimensional and nonhyperbolic in both models.

Topologies of critical spaces differ significantly between models.

Nondiagonal case may exhibit a new form of chaos.

Abstract

We make comparison of the dynamics of the diagonal and nondiagonal Bianchi IX models in the evolution towards the cosmological singularity. Apart from the original variables, we use the Hubble normalized ones commonly applied in the examination of the dynamics of homogeneous models. Applying the dynamical systems method leads to the result that in both cases the continuous space of critical points is higher dimensional and they are of the nonhyperbolic type. This is a generic feature of the dynamics of both cases and seems to be independent on the choice of phase space variables. The topologies of the corresponding critical spaces are quite different. We conjecture that the nondiagonal case may carry a new type of chaos different from the one specific to the usually examined diagonal one.