  The presence of the large-scale magnetic fields is one of the greatest
puzzles of contemporary cosmology. The symmetries of the electromagnetic field
theory combined with the geometric structure of the FRW universe leads to an
adiabatic decay of the primordial magnetic fields. Due to this rapid decay the
residual large scale magnetic field is astrophysically unimportant. A common
feature among many of the proposed amplification mechanisms is the violation of
Lorentz symmetries. We introduce an amplification mechanism within a Lorentz
violating environment where we use Finsler geometry as our theoretical
background. The mechanism is based on the adoption of a local anisotropic
structure that leads to modifications on the Ricci identities. Thus, the
wave-like equation of any vector source, including the magnetic field, is
enriched by the Finslerian curvature theory. In particular limits the remaining
seed field can be strong enough to seed the galactic dynamo. In our analysis we
also develop the 1+3 covariant formalism for the 4-vector potential in curved
space-times.
