Gravitational Instability of Yang-Mills Cosmologies

TL;DR

This paper investigates the gravitational stability of Yang-Mills cosmologies using numerical methods, revealing initial dilution of fluctuations followed by complex nonlinear growth and inhomogeneity over time.

Contribution

It provides a numerical analysis of the long-term nonlinear evolution and instability of Yang-Mills fields in cosmological settings.

Findings

Initial energy dilution due to conformal invariance

Transition to inhomogeneous expansion

Growth of energy contrasts and nonlinear regime

Abstract

The gravitational instability of Yang-Mills cosmologies is numerically studied with the hamiltonian formulation of the spherically symmetric Einstein-Yang-Mills equations with SU(2) gauge group. On the short term, the expansion dilutes the energy densities of the Yang-Mills fluctuations due to their conformal invariance. In this early regime, the gauge potentials appear oscillating quietly in an interaction potential quite similar to the one of the homogeneous case. However, on the long term, the expansion finally becomes significantly inhomogeneous and no more mimics a conformal transformation of the metric. Thereafter, the Yang-Mills fluctuations enter a complex non-linear regime, accompanied by diffusion, while their associated energy contrasts grow.