Cosmological magnetic fields from inflation in extended electromagnetism
  In this work we consider an extended electromagnetic theory in which the
scalar state which is usually eliminated by means of the Lorenz condition is
allowed to propagate. This state has been shown to generate a small
cosmological constant in the context of standard inflationary cosmology. Here
we show that the usual Lorenz gauge-breaking term now plays the role of an
effective electromagnetic current. Such a current is generated during inflation
from quantum fluctuations and gives rise to a stochastic effective charge
density distribution. Due to the high electric conductivity of the cosmic
plasma after inflation, the electric charge density generates currents which
give rise to both vorticity and magnetic fields on sub-Hubble scales. Present
upper limits on vorticity coming from temperature anisotropies of the CMB are
translated into lower limits on the present value of cosmic magnetic fields. We
find that, for a nearly scale invariant vorticity spectrum, magnetic fields
$B_{\lambda}> 10^{-12}$ G are typically generated with coherence lengths
ranging from sub-galactic scales up to the present Hubble radius. Those fields
could act as seeds for a galactic dynamo or even account for observations just
by collapse and differential rotation of the protogalactic cloud.
