Revisiting Magnetogenesis during Inflation

TL;DR

This paper analyzes the stochastic dynamics of electromagnetic fields during inflation, revealing conditions under which primordial magnetic fields can be amplified and stabilized, potentially explaining observed cosmic magnetic fields.

Contribution

It introduces a stochastic noise framework for magnetogenesis during inflation, deriving analytical Langevin and Fokker-Planck equations to explore magnetic field evolution.

Findings

Magnetic fields can reach amplitudes of ~10^{-13} Gauss today.

Stochastic effects can lead to a mean-reverting magnetic field behavior.

Backreactions can be controlled to allow significant magnetic field generation.

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, but 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 $\sim 10^{-13}$ Gauss and coherent length ${\rm Mpc}$ can be generated while the backreactions of the electric field perturbations are under control.