Chaos in Anisotropic Pre-Inflationary Universes

TL;DR

This paper investigates how anisotropy and a cosmological constant in early universe models can lead to chaotic dynamics, affecting inflation and fluctuation amplification, with a focus on the phase space structure.

Contribution

It demonstrates that anisotropic Bianchi type-IX models with matter and cosmological constant exhibit chaos due to saddle-center points, providing a geometric interpretation of Wald's inequality.

Findings

Chaos arises from saddle-center critical points in the phase space.

Invariant chaos is maintained by the topology of cylinders from unstable periodic orbits.

Mechanism for amplification of inhomogeneous fluctuations is discussed.

Abstract

We study the dynamics of anisotropic Bianchi type-IX models with matter and cosmological constant. The models can be thought as describing the role of anisotropy in the early stages of inflation. The concurrence of the cosmological constant and anisotropy are sufficient to produce a chaotic dynamics in the gravitational degrees of freedom, connected to the presence of a critical point of saddle-center type in the phase space of the system. The invariant character of chaos is guaranteed by the topology of the cylinders emanating from unstable periodic orbits in the neighborhood of the saddle-center. We discuss a possible mechanism for amplification of specific wavelengths of inhomogeneous fluctuations in the models. A geometrical interpretation is given for Wald's inequality in terms of invariant tori and their destruction by increasing values of the cosmological constant.