We present a complete numerical treatment of inflationary dynamics under the influence of stochastic corrections from sub-Hubble modes. We discuss how to exactly model the stochastic noise terms arising from the sub-Hubble quantum modes that give rise to the coarse-grained inflaton dynamics in the form of stochastic differential equations. The stochastic differential equations are solved event-by-event on a discrete time grid. We then compute the power spectrum of curvature perturbations that can be compared with the power spectrum computed in the traditional fashion using the Mukhanov-Sasaki equation by canonically quantizing the inflaton fluctuations. Our numerical procedure helps us to easily extend the formalism to ultra slow-roll inflation and study the possibility of primordial black hole formation.

中文翻译：

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对慢滚及以后的随机通货膨胀进行数值模拟

我们在亚哈勃模式的随机修正的影响下，对暴胀动力学进行了完整的数值处理。我们讨论了如何以随机微分方程的形式对由亚哈勃量子模式产生的随机噪声项进行精确建模，这些模式引起粗粒度暴胀子动力学。随机微分方程在离散时间网格上逐事件求解。然后我们计算曲率扰动的功率谱，该功率谱可以与使用 Mukhanov-Sasaki 方程通过规范量化暴胀子波动以传统方式计算的功率谱进行比较。我们的数值程序帮助我们轻松地将形式主义扩展到超慢滚膨胀，并研究原始黑洞形成的可能性。