Decay of Magnetic Fields in the Early Universe∗

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 ξ, magnetic energy EM and magnetic helicity H evolve with time. We show that the self-similarity of the magnetic power spectrum alone implies that ξ ∼ t1/2. This in turn implies that magnetic helicity decays as H ∼ t−2s , and that the magnetic energy decays as EM ∼ t −0.5−2s , where s is inversely proportional to the magnetic Reynolds number ReM. These laws improve on several previous estimates. SUSX-TH-03-002 NORDITA-2003-5 AP