Cosmological magnetic helicity and birefrigence from primordial torsion
  in Lorentz violation theories
  Cosmological magnetic helicity has been thought to be a fundamental agent for
magnetic field amplification in the universe. More recently Semikoz and
Sokoloff [Phys Rev Lett 92 (2004): 131.301.] showed that the weakness of the
seed fields did not necessarily imply the weakness of magnetic cosmological
helicity. In this paper we present a derivation of dynamo equation based upon
the flat torsion photon non-minimal coupling through Riemann-Cartan spacetime.
From this derivation one computes the necessary conditions for a flat torsion
field to generate a galactic dynamo seed, from the cosmological magnetic
helicity. A peculiar feature of this dynamo equation is that the resistivity
depends upon the Ricci scalar curvature. This feature is also present in
turbulent dynamo models. Here the electrical effective conductivity is obtained
by making use of flat torsion modes of a $R(\Gamma)F^{2}$ Lagrangean where R
refers to the Ricci-Cartan spacetime. Power spectrum of the magnetic field is
also computed. Lorentz violation appears naturally from birefrigence of photons
semi-minimally coupled to torsion. Though Dobado and Maroto [Mod Phys Lett A
12: 3003 (1997)] have previously investigated the role of primordial torsion in
the anisotropy of light propagation they made it using the fermionic sector of
the QED Lagrangean while we obtained similar results using the photonic sector.
They also used the pseudo-trace of torsion while we here work out with the
torsion trace itself.
