Influence of Tachyonic Instability on the Schwinger Effect by Axial Coupling in Natural Inflation Model When Strong Back-Reaction Exists

Abstract

The influence of tachyonic instability on the Schwinger effect is investigated by axial coupling in the natural single-field inflation model when strong back-reaction exists in two parts. First, the Schwinger effect is considered when the conformal invariance of Maxwell action should be broken by axial coupling $I\left(\varphi \right)F_{\mu \nu }{\stackrel{\sim }{F}}^{\mu \nu }$ 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. It has been found 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. Two coupling functions are used to break conformal invariance of maxwell action. The simplest coupling function $I\left(\varphi \right)={\chi }_1\frac{\varphi }{M_p}$ and a curvature based coupling function $I\left(\varphi \right)=12{\chi }_1{e}^{\left(\sqrt{\frac{2}{3}},\frac{\varphi }{M_p}\right)}\left(\frac{1}{3M_p^2},\left(4,V,\left(\varphi \right)\right),+,\frac{\sqrt{2}}{\sqrt{3}{M}_p},\left(\frac{dV}{d\varphi }\right)\right)$ where $V\left(\varphi \right)$ is the potential of natural inflation. In second part, in oder to avoid strong back-reaction problem, the horizon scale $k_H=aH\left|\zeta \right|,\zeta =\frac{I^{\prime }\left(\varphi \right)\dot{\varphi }}{H}$ is identified in which a given Fourier begins to become tachyonically unstable.The influence 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. Therefore, the Schwinger effect in this model is not possible and spoils inflation. Instantly, the Schwinger effect produces very high energy density of charged particles which causes back-reaction problem and spoils inflaton field. It has been stressed that due to existence of strong back-reaction in two cases the energy density of the produced charged particles due to the Schwinger effect spoils inflation. The influence of tachyonic instability in this model is quiet different from our published work in Kamarpour. In Kamarpour, this effect appears by vanishing of electromagnetic energy density and the energy density of charged particles at the very beginning of inflation.