Axially Symmetric Bianchi I Yang-Mills Cosmology as a Dynamical System

TL;DR

This paper develops a comprehensive model of axially symmetric SU(2)-Yang-Mills fields in Bianchi cosmologies, analyzing their dynamical behavior and stochastic properties compared to electromagnetic and isotropic YM fields.

Contribution

It introduces the most general axially symmetric SU(2)-Yang-Mills fields in Bianchi cosmologies and compares their dynamics and stochasticity with other cosmological models.

Findings

Bianchi I-EYM system exhibits milder stochastic properties than flat YM system.

Liapunov exponent is non-zero in conformal time, indicating chaos.

Numerical analysis of Liapunov exponents supports the dynamical differences.

Abstract

We construct the most general form of axially symmetric SU(2)-Yang-Mills fields in Bianchi cosmologies. The dynamical evolution of axially symmetric YM fields in Bianchi I model is compared with the dynamical evolution of the electromagnetic field in Bianchi I and the fully isotropic YM field in Friedmann-Robertson-Walker cosmologies. The stochastic properties of axially symmetric Bianchi I-Einstein-Yang-Mills systems are compared with those of axially symmetric YM fields in flat space. After numerical computation of Liapunov exponents in synchronous (cosmological) time, it is shown that the Bianchi I-EYM system has milder stochastic properties than the corresponding flat YM system. The Liapunov exponent is non-vanishing in conformal time.