The Schwinger effect by axial coupling in natural inflation model

TL;DR

This paper examines the Schwinger effect with axial coupling in natural inflation, finding that strong back-reaction prevents the effect from occurring effectively, regardless of the coupling function used.

Contribution

It introduces a detailed analysis of the Schwinger effect in natural inflation with axial coupling, highlighting the back-reaction problem and proposing a scale to mitigate it.

Findings

High energy density of produced particles spoils inflation

Back-reaction prevents effective Schwinger effect

Scaling the horizon reduces coupling but does not eliminate back-reaction

Abstract

We investigate the process of the Schwinger effect by axial coupling in the natural single-field inflation model in two parts. First we consider the Schwinger effect when the conformal invariance of Maxwell action should be broken by axial coupling $ I(\phi)F_{\mu\nu}\tilde{F}^{\mu\nu} $ with the inflaton field by identifying the standard horizon scale $ k=aH $ at the very beginning of inflation for additional boundary term and use several values of coupling constant $ \chi_{1} $ and estimate electric and magnetic energy densities and energy density of produced charged particles due to the Schwinger effect.We find that for both coupling functions the energy density of the produced charged particles due to the Schwinger effect is so high and spoils inflaton field.In fact the strong coupling or back-reaction occurs because the energy density of produced charged particles is exceeding of inflaton field.We use two coupling functions to break conformal invariance of maxwell action.The simplest coupling function $ I\left(\phi\right)=\chi_{1}\frac{\phi}{M_{p}} $ and a curvature based coupling function $ I\left(\phi\right)= 12\chi_{1}e^{\left(\sqrt{\frac{2}{3}}\frac{\phi}{M_{p}}\right)}\left[\frac{1}{3M_{p}^{2}}\left(4V\left(\phi\right)\right)+\frac{\sqrt{2}}{\sqrt{3}M_{p}}\left(\frac{dV}{d\phi}\right)\right] $ where $V\left(\phi\right) $ is the potential of natural inflation. In second part , in oder to avoid strong back-reaction problem we identify the horizon scale $ k_{H}=aH|\zeta| , \zeta=\frac{{I}^{\prime}\left(\phi\right)\dot{\phi}}{H} $ in which a given Fourier begins to become tachyonically unstable.The effect of this scale is reducing the value of coupling constant $ \chi_{1} $ and weakening the back-reaction problem but in both cases strong coupling or strong back-reaction exists and the Schwinger effect is impossible.