  We present new simulations of decaying hydromagnetic turbulence for a
relativistic equation of state relevant to the early universe. We compare
helical and nonhelical cases either with kinetically or magnetically dominated
initial fields. Both kinetic and magnetic initial helicities lead to maximally
helical magnetic fields after some time, but with different temporal decay
laws. Both are relevant to the early universe, although no mechanisms have yet
been identified that produce magnetic helicity with strengths comparable to the
big bang nucleosynthesis limit at scales comparable to the Hubble horizon at
the electroweak phase transition. Nonhelical magnetically dominated fields
could still produce picoGauss magnetic fields under most optimistic conditions.
Only helical magnetic fields can potentially have nanoGauss strengths at scales
up to 30 kpc today.
