Time Evolution of the Large-Scale Tail of Nonhelical Primordial Magnetic
  Fields with Back-Reaction of the Turbulent Medium
  We present a derivation of the time evolution equations for the energy
content of nonhelical magnetic fields and the accompanying turbulent flows from
first principles of incompressible magnetohydrodynamics in the general
framework of homogeneous and isotropic turbulence. This is then applied to the
early Universe, i.e., the evolution of primordial magnetic fields. Numerically
integrating the equations, we find that most of the energy is concentrated at
an integral wavenumber scale k_I where the turbulence turn over time equals the
Hubble time. At larger length scales L, i.e., smaller wavenumbers q = 2 \pi / L
<< k_I, independent of the assumed turbulent flow power spectrum, mode-mode
coupling tends to develop a small q magnetic field tail with a Batchelor
spectrum proportional to the fourth inverse power of L and therefore a scaling
for the magnetic field of B ~ L^(-5/2).
