Decay of Magnetic Fields in the Early Universe

Abstract

We study the evolution of a stochastic helical magnetic field generated in the early Universe after the electroweak phase transition, using standard magnetohydrodynamics (MHD). We find how the coherence length xi, magnetic energy E_M and magnetic helicity H evolve with time. We show that the self-similarity of the magnetic power spectrum alone implies that xi ~ t^{1/2}. This in turn implies that magnetic helicity decays as H ~ t^{-2s}, and that the magnetic energy decays as E_M ~ t^{-0.5-2s}, where s is inversely proportional to the magnetic Reynolds number Re_M. These laws improve on several previous estimates.