标题： 轴向耦合在自然暴胀模型中的施温格效应 显示英文标题

标题： The Schwinger effect by axial coupling in natural inflation model

摘要： 我们通过轴向耦合在自然单场暴胀模型中分两部分研究了施温格效应的过程。 首先我们考虑当麦克斯韦作用量的共形不变性应通过轴向耦合 $ I(\phi)F_{\mu\nu}\tilde{F}^{\mu\nu} $ 与暴胀场结合而被破坏时的施温格效应，通过在暴胀刚开始时识别标准视界尺度 $ k=aH $ 作为额外边界项，并使用几个耦合常数 $ \chi_{1} $ 的值，估计由于施温格效应产生的电能密度和磁能密度以及带电粒子的能量密度。我们发现对于这两种耦合函数，由于施温格效应产生的带电粒子的能量密度非常高，从而破坏了暴胀场。事实上，因为产生的带电粒子的能量密度超过了暴胀场的能量密度，所以出现了强耦合或反作用。我们使用两种耦合函数来破坏麦克斯韦作用量的共形不变性。最简单的耦合函数 $ I\left(\phi\right)=\chi_{1}\frac{\phi}{M_{p}} $ 和一个基于曲率的耦合函数 $ 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] $ ，其中 $V\left(\phi\right) $ 是自然暴胀的势能。 在第二部分中，为了避开强烈的反作用问题，我们确定了视界尺度$ k_{H}=aH|\zeta| , \zeta=\frac{{I}^{\prime}\left(\phi\right)\dot{\phi}}{H} $，在该尺度上，给定的傅里叶模开始变得超光速不稳定。这个尺度的影响是降低耦合常数$ \chi_{1} $的值并减弱反作用问题，但在这两种情况下都存在强耦合或强反作用，因此无法产生施温格效应。 显示英文摘要

摘要： 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.