AI 中文总结
研究某类结合Starobinsky模型和α吸引子模型性质的E模型中暴胀标量场动力学，用慢滚近似等方法获解析表达式，导出Hill方程研究微扰演化，发现宇宙学膨胀限制标量模式共振增长，张量涨落无共振放大。
AI 中文摘要
我们研究了一类结合了Starobinsky模型和α吸引子模型性质的暴胀E模型中暴胀标量场的动力学。所处理的暴胀势在高场值处有指数平坦的平台，在零处有明确的最小值。利用慢滚近似，我们得到了描述暴胀阶段背景暴胀场演化的解析表达式。为描述预热阶段的非线性场振荡，我们使用了快速（振荡相位）和慢速（场能量密度）变量分离技术。所得表达式与场方程的直接数值积分结果吻合良好。这些表达式随后被用于研究预热阶段的微扰演化。基于Mukhanov-Sasaki方程，我们导出了具有缓慢变化参数的Hill方程，它描述了考虑背景振荡非谐性的标量微扰模式。利用Floquet理论，我们分析了该方程共振区的结构并进行了数值积分。我们表明宇宙学膨胀限制了标量模式的共振增长，使其振幅在后期几乎恒定。我们还导出了张量模式的相应Hill方程。我们表明度规张量涨落的共振放大不会发生。
英文摘要
We investigate the dynamics of the inflaton scalar field in a certain class of inflationary E-models that combine the properties of the Starobinsky model and the $α$-attractor model. The inflaton potential we are dealing with has an exponentially flat plateau at high field values and a sharply defined minimum at zero. Using the slow-roll approximation, we obtain the analytic expressions describing evolution of the background inflaton field at the inflationary stage. To describe the nonlinear field oscillations at the preheating stage, we use the technique of separation of fast (oscillation phase) and slow (field energy density) variables. The obtained expressions are in good agreement with the results of direct numerical integration of the field equations. These expressions are then used to study the evolution of perturbations at the preheating stage. Based on the Mukhanov-Sasaki equation, we derive the Hill equation with slowly varying parameters, which describes the scalar perturbation modes taking into account the anharmonicity of the background oscillations. Using Floquet theory, we analyze the structure of the resonance zones of this equation and then integrate it numerically. We show that the cosmological expansion limits the resonant growth of scalar modes, making their amplitudes nearly constant at late times. We also derive the corresponding Hill equation for tensor modes. We show that resonant amplification of tensor fluctuations of the metric does not occur.
Comments9 pages, 12 figures
