  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.
