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

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.