The (In)stability of Bianchi IX Dynamics: Geodesic Deviation Equations in Finsler Spaces

TL;DR

This paper investigates the stability of Bianchi IX cosmological models using Finsler geometry, revealing no traditional chaos but indicating a chaotic scattering scenario through numerical geodesic analysis.

Contribution

It introduces a gauge-invariant, unapproximated geometric approach to analyze Bianchi IX dynamics within Finsler spaces, providing new insights into their stability properties.

Findings

No traditional chaos signatures found in geodesic analysis.

Evidence of chaotic scattering dynamics in Bianchi IX models.

Geometrical framework offers a novel perspective on cosmological stability.

Abstract

We explore the dynamical stability of the minisuperspace Hamiltonian of the Bianchi IX cosmological models, giving a gauge-invariant and unapproximated description of the full continuous dynamics, achieved through a geometrical description of the equations of motion in the framework of the theory of Finsler Spaces. The numerical integrations of the geodesics and geodesic deviation equations show clearly the absence of any "traditional" signature of Chaos, while suggesting a chaotic scattering dynamics scenario.