Magnetic field amplification by the small-scale dynamo in the early
  Universe
  In this paper we show that the Universe is already strongly magnetized at
very early epochs during cosmic evolution. Our calculations are based on the
efficient amplification of weak magnetic seed fields, which are unavoidably
present in the early Universe, by the turbulent small-scale dynamo. We identify
two mechanisms for the generation of turbulence in the radiation dominated
epoch where velocity fluctuations are produced by the primordial density
perturbation and by possible first-order phase transitions at the electroweak
or QCD scales. We show that all the necessities for the small-scale dynamo to
work are fulfilled. Hence, this mechanism, operating due to primordial density
perturbations, guarantees fields with comoving field strength
$B_0\sim10^{-6}\varepsilon^{1/2}$ nG on scales up to $\lambda_c\sim0.1$ pc,
where $\varepsilon$ is the saturation efficiency. The amplification of magnetic
seed fields could be even larger if there are first-order phase transitions in
the early Universe. Where, on scales up to $\lambda_c\sim100$ pc, the comoving
field strength due to this mechanism will be $B_0\sim10^{-3}\varepsilon^{1/2}$
nG at the present time. Such fields, albeit on small scales, can play an
important role in structure formation and could provide an explanation to the
apparently observed magnetic fields in the voids of the large-scale structure.
