The Schwinger effect and natural inflationary magnetogenesis

We investigate the process of inflationary magnetogenesis in the natural single-field inflation model in two parts. First we switch off the Schwinger effect and consider the conformal invariance of Maxwell action should be broken by kinetic coupling I-2(phi)F-mu nu F-mu nu with the inflation field and the coupling function as a power of a scale factor, I (phi) proportional to a(alpha), and alpha < 0 must be used in order to avoid the back-reaction problem. For such alpha, the electric component of the energy density dominates the magnetic one because I (phi) is decreasing function of time during inflation and, for alpha? -2.2, it causes strong back-reaction which can spoil inflation and terminate the enhancement of the magnetic field. When we switch on the Schwinger effect, there is difference in background inflation field. Therefore, the Schwinger effect in this model has alteration in magneto-genesis. The Schwinger effect decreases the value of the electric field and helps to finish the inflation stage and enter the stage of preheating. It considerably and effectively produces the charged particles, implementing the Schwinger reheating framework-scenario even before the fast oscillations of the inflation field. The numericaI results in both parts carried out in natural single-field inflation model with coupling function I(phi) = cos(alpha beta) (phi/2f) where alpha is coupling parameter and beta = 2f(2)/M-p(2) .