Primordial magnetic fields from inflation?
  The hot plasma above the electroweak scale contains (hyper) charged scalar particles which are coupled to Abelian gauge fields. Scalars may interact with gravity in a non-conformally invariant way and thus their fluctuations can be amplified during inflation. These fluctuations lead to creation of electric currents and produce inhomogeneous distribution of charge density, resulting in the generation of cosmological magnetic fields. We address the question whether these fields can be coherent at large scales so that they may seed the galactic magnetic fields. Depending upon the mass of the charged scalar and upon various cosmological (critical fraction of energy density in matter, Hubble constant) and particle physics parameters we found that the magnetic fields generated in this way are much larger than vacuum fluctuations. However, their amplitude on cosmological distances is found to be too small for seeding the galactic magnetic fields. 
M.Giovannini and M. Shaposhnikov (Institute for Theoretical Physics,   Lausanne University)