Cosmological magnetogenesis from extra-dimensional Gauss-Bonnet gravity

Abstract

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.