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(phi) proportional to a(alpha), and alpha < 0 is used in order to avoid the strong coupling problem. For such.., the electric component of the energy density dominates over the magnetic one and, for alpha less than or similar to -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 similar to 10(-20) G at the present epoch, and their spectrum has a blue tilt.