Chaotic dynamics of the Bianchi IX universe in Gauss-Bonnet gravity

TL;DR

This paper explores the chaotic behavior of anisotropic Bianchi IX universes with Gauss-Bonnet gravity, revealing how mode interactions lead to unpredictable cosmic evolution near critical points.

Contribution

It demonstrates that the inclusion of anisotropy and higher curvature terms induces chaos in Bianchi IX cosmologies, unlike simpler models.

Findings

Chaos arises from mode interactions near the critical point.

Fractal basin structures indicate sensitive dependence on initial conditions.

Anisotropy introduces rotational modes that interact with hyperbolic modes.

Abstract

We investigate the dynamics of closed FRW universe and anisotropic Bianchi type-IX universe characterized by two scale factors in a gravity theory including a higher curvature (Gauss-Bonnet) term. The presence of the cosmological constant creates a critical point of saddle type in the phase space of the system. An orbit starting from a neighborhood of the separatrix will evolve toward the critical point, and it eventually either expands to the de Sitter space or collapses to the big crunch. In the closed FRW model, the dynamics is reduced to hyperbolic motions in the two-dimensional center manifold, and the system is not chaotic. In the anisotropic model, anisotropy introduces the rotational mode, which interacts with the hyperbolic mode to present a cylindrical structure of unstable periodic orbits in the neighborhood of the critical point. Due to the non-integrability of the system, the interaction of rotational and hyperbolic modes makes the system chaotic, making it impossible for us to predict the final fate of the universe. We find that the chaotic dynamics arises from the fact that orbits with even small perturbations around the separatrix oscillate in the neighborhood of the critical point before finally expanding or collapsing. The chaotic character is also evidenced by the fractal structures in the basins of attraction.