Magnetic Fields in the Early Universe

The observed galactic magnetic fields may have a primordial origin. I briefly review the observations, their interpretation in terms of the dynamo theory, and the current limits on cosmological magnetic fields. Several possible mechanisms for generating a primordial magnetic field are then discussed. Turbulence and the evolution of the microscopic fields to macroscopic fields is described in terms of a shell model, which provides an approximation to the full magnetohydrodynamics and indicates the existence of an inverse cascade of magnetic energy. Cosmological seed fields roughly of the order of $10^{-20}$ G at the scale of protogalaxy, as required by the dynamo explanation of galactic magnetic fields, seem rather plausible.