The Evolution of the Large-Scale Tail of Primordial Magnetic Fields
  Cosmic magnetic fields may be generated during early cosmic phase transition,
such as the QCD- or electroweak- transitions. The magnitude of the remainder of
such fields at the present epoch crucially depends on the exponent $n$ of their
(initially super-Hubble) large-scale tail, i.e. B(lambda) ~ lambda^(-n). It has
been claimed that causality requires n=5/2, contrary to much earlier claims of
n=3/2. Here we analyze this question in detail. First, we note that contrary to
current belief, the large-scale magnetic field tail is not established at the
phase transition itself, but rather continuoulsy evolves up to the present
epoch. Neglecting turbulent flows we find n=7/2, i.e. very strongly suppressed
large-scale fields. However, in the inevitable presence of turbulent flows we
find that the large-scale magnetic field tail has sufficient time to evolve to
that of the fluid turbulence. For white noise fluid turbulence this yields
n=3/2 up to a certain scale and n=5/2 beyond for the magnetic field spectrum.
This picture is also not changed when primordial viscosity and fluid flow
dissipation is taken into account. Appreciable primordial magnetic fields
originating from cosmic phase transitions seem thus possible.
