Cosmological Magnetogenesis From Extra-dimensional Gauss Bonnet Gravity
  Generation of primordial magnetic fields during inflation typically requires
the breaking of conformal invariance of the Electromagnetic action. In this
paper this has been achieved naturally in a higher dimensional cosmological
model with a Gauss-Bonnet term in the action. The evolution of the scale factor
of the extra dimension (whose dynamics is influenced by the Gauss-Bonnet term)
acts as the cause for the breaking of conformal invariance. Different cases
have been investigated, each of which is characterized by the number of higher
dimensions, the value of the Gauss-Bonnet parameter, and the cosmological
constant. Many of the scenarios considered are highly constrained by the
requirements that the cosmic evolution is stable, that the normal dimensions
expand and that there is no back reaction due to growing electric fields.
However there do exist scenarios which satisfy the above requirements and are
well suited for magnetogenesis. In particular, a scenario where the number of
extra dimensions $D=4$ and the cosmological constant is non-zero, turns out to
be best suited for generating primordial magnetic fields. It is shown that for
these values of parameters, a scale invariant magnetic field of the order of
$10^{-10}-10^{-9}$ $G$ can be produced. Even in these most favorable scenarios,
the higher dimensional space expands during inflation at the same rate as the
normal dimension. Hence if a mechanism could freeze the evolution of the higher
dimension, this seems to be a viable mechanism to produce acceptable primordial
magnetic fields.
