Revisiting magnetogenesis during inflation

Abstract

We revisit the mechanism of primordial magnetogenesis during inflation by taking into account the dynamics of the stochastic noises of the electromagnetic perturbations. We obtain the associated Langevin and Fokker-Planck equations for the electromagnetic fields and solve them analytically. It is shown that while the backreactions of the electric field energy density may spoil inflation too early, there are regions of parameter space where the usual decaying behavior of the magnetic fields are replaced by a mean-reverting process of stochastic dynamics. As a result the magnetic fields settle down into an equilibrium state with the amplitude significantly larger than what is obtained in the absence of the stochastic noises. We show that magnetic fields with present time amplitude $\ensuremath{\sim}{10}^{\ensuremath{-}13}$ Gauss and correlation length Mpc can be generated while the backreactions of the electric field perturbations are under control.