Stability of large scale chromomagnetic fields in the early universe

Abstract

It is well known that Yang-Mills theory in vacuum has a perturbative instability to spontaneously form a large scale magnetic field (the Savvidy mechanism) and that a constant field is unstable so that a possible ground state has to be inhomogenous over the non-perturbative scale Λ (the Copenhagen vacuum). We argue that this spontaneous instability does not occur at high temperature when the induced field strength gB ∼ Λ 2 is much weaker than the magnetic mass squared ( g 2 T) 2. At high temperature, oscillations of gauge fields acquire a thermal mass M ∼ gT and we show that this mass stabilizes a magnetic field which is constant over length scales shorter than the magnetic screening length ( g 2 T) −1. We therefore conclude that there is no indication for any spontaneous generation of weak non-abelian magnetic fields in the early universe.