  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.
