Magnetogenesis in Natural Inflation Model

We study the process of inflationary magnetogenesis in the natural single-field inflation model, whose parameters are chosen in accordance with the recent observations by the Planck collaboration [1]. The conformal invariance of the Maxwell action is broken by a kinetic coupling with the inflaton field by means of the coupling function as a power of the scale factor, I(ф) ∝ aa, and a < 0 is used in order to avoid the strong coupling problem. For such a, the electric component of the energy density dominates over the magnetic one and, for a <- −2.2, it causes a strong back-reaction, which can spoil inflation and terminate the enhancement of the magnetic field. It is found that the magnetic fields generated without back-reaction problem cannot exceed ∼10−20G at the present epoch, and their spectrum has a blue tilt.