A nonzero primordial vorticity seeds a hypermagnetic field from zero in the symmetric phase; the chiral magnetic effect then amplifies it and converts lepton into baryon asymmetry.
Magnetohydrodynamics of the Early Universe and the Evolution of Primordial Magnetic Fields
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We show that the decaying magnetohydrodynamic turbulence leads to a more rapid growth of the correlation length of a primordial magnetic field than that caused by the expansion of the Universe. As an example, we consider the magnetic fields created during the electroweak phase transition. The expansion of the universe alone would yield a correlation length at the present epoch of 1 AU, whereas we find that the correlation length is likely of order 100 AU, and cannot possibly be longer than $10^4$ AU for non-helical fields. If the primordial field is strongly helical, the correlation length can be much larger, but we show that even in this case it cannot exceed 100 pc. All these estimates make it hard to believe that the observed galactic magnetic fields can result from the amplification of seed fields generated at the electroweak phase transition by the standard galactic dynamo.
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Contribution of the chiral vortical effect to the evolution of the hypermagnetic field and the matter-antimatter asymmetry in the early Universe
A nonzero primordial vorticity seeds a hypermagnetic field from zero in the symmetric phase; the chiral magnetic effect then amplifies it and converts lepton into baryon asymmetry.