On the Physics of Primordial Magnetic Fields
  There are at present more then 30 theories about the origin of cosmic magnetic fields at galactic and intergalactic scales. Most of them rely on concepts of elementary particle physics, like phase transitions in the early Universe, string theory and processes during the inflationary epoch. Here we present some more astrophysical arguments to provide some guidance through this large number and variety of models. Especially the fact that the evolution of magnetic fields depends on the spatial coherence scale of the fields leds to some interesting conclusions, which may rule out the majority of the theoretical scenarios. In principle one has to distinguish between the large-scale and small-scale magnetic fields. Large scale fields are defined as those as becoming sub-horizon at that redshift at which the mass energy density becomes equal to the photon energy density, which we name as equality. Small scale fields which are sub-horizon even before equality, i.e. with scales lower than (present) few Mpc cannot survive the radiation era and cannot reach recombination, because of the effects of magnetic diffusion and photon diffusion. Therefore mechanisms based on phase transitions become unlike, as they provide magnetic fields on scales smaller than the horizon. Thus, the observed galactic and intergalactic fields, which are small scales in our terminology must be created after recombination by normal plasma processes during the protogalactic evolution. The large scale fields instead were produced during inflation and may have noticeable implications for the formation of the large scale structure of the Universe. The inclusion of large scale magnetic fields may improve present Cold Dark Matter theories of structure formation. 
E. Battaner & H. Lesch