Cosmological Magnetic Field: a fossil of density perturbations in the   early universe
  The origin of the substantial magnetic fields that are found in galaxies and on even larger scales, such as in clusters of galaxies, is yet unclear. If the second-order couplings between photons and electrons are considered, then cosmological density fluctuations, which explain the large scale structure of the universe, can also produce magnetic fields on cosmological scales before the epoch of recombination. By evaluating the power spectrum of these cosmological magnetic fields on a range of scales, we show here that magnetic fields of 10^{-18.1} gauss are generated at a 1 megaparsec scale and can be even stronger at smaller scales (10^{-14.1} gauss at 10 kiloparsecpc). These fields are large enough to seed magnetic fields in galaxies and may therefore have affected primordial star formation in the early universe. 
Kiyotomo Ichiki, Keitaro Takahashi, Hiroshi Ohno, Hidekazu Hanayama,   Naoshi Sugiyama