Influence of backreaction of electric fields and Schwinger effect on inflationary magnetogenesis

Understand

We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling $f^{2}(\phi)F_{\mu\nu}F^{\mu\nu}$ of the electromagnetic field to the inflaton field $\phi$.

• We consider the case where the coupling function $f(\phi)$ decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one.
• The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived.
• The backreaction occurs when the electric energy density becomes as large as the product of the slow-roll parameter $\epsilon$ and inflaton energy density, $\rho_{E}\sim \epsilon \rho_{\rm inf}$.