Large-Scale Magnetic Fields, Dark Energy and QCD
  Cosmological magnetic fields are being observed with ever increasing
correlation lengths, possibly reaching the size of superclusters, therefore
disfavouring the conventional picture of generation through primordial seeds
later amplified by galaxy-bound dynamo mechanisms. In this paper we put forward
a fundamentally different approach that links such large-scale magnetic fields
to the cosmological vacuum energy. In our scenario the dark energy is due to
the Veneziano ghost (which solves the $U(1)_A$ problem in QCD). The Veneziano
ghost couples through the triangle anomaly to the electromagnetic field with a
constant which is unambiguously fixed in the standard model. While this
interaction does not produce any physical effects in Minkowski space, it
triggers the generation of a magnetic field in an expanding universe at every
epoch. The induced energy of the magnetic field is thus proportional to
cosmological vacuum energy: $\rho_{EM}\simeq B^2 \simeq (\frac{\alpha}{4\pi})^2
\rho_{DE}$, $\rho_{DE}$ hence acting as a source for the magnetic energy
$\rho_{EM}$. The corresponding numerical estimate leads to a magnitude in the
nG range. There are two unique and distinctive predictions of our proposal: an
uninterrupted active generation of Hubble size correlated magnetic fields
throughout the evolution of the universe; the presence of parity violation on
the enormous scales $1/H$, which apparently has been already observed in CMB.
These predictions are entirely rooted into the standard model of particle
physics.
