Chaos in the Einstein-Yang-Mills Equations
John D. Barrow, Janna Levin
TL;DR
This paper investigates chaotic dynamics in Yang-Mills fields within an expanding universe, revealing persistent chaos and isotropization, with a novel fractal basin boundary method to characterize chaos.
Contribution
It introduces a coordinate-independent way to characterize chaos in cosmological Yang-Mills fields using fractal basin boundaries.
Findings
Yang-Mills fields exhibit chaotic evolution in anisotropic expansion.
The universe tends to isotropize at late times despite ongoing chaos.
Fractal basin boundaries effectively characterize the chaos in the system.
Abstract
Yang-Mills color fields evolve chaotically in an anisotropically expanding universe. The chaotic behaviour differs from that found in anisotropic Mixmaster universes. The universe isotropizes at late times, approaching the mean expansion rate of a radiation-dominated universe. However, small chaotic oscillations of the shear and color stresses continue indefinitely. An invariant, coordinate-independent characterisation of the chaos is provided by means of fractal basin boundaries.
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