标题： 暴胀动力学的数值模拟：慢滚与超越 显示英文标题

标题： Numerical simulations of inflationary dynamics: slow roll and beyond

摘要： 本文展示了关于单一规范标量场（该标量场最小耦合到引力）的膨胀动力学的数值模拟。 我们以宇宙时间为变量$t$来阐述控制膨胀动力学的基本方程，并定义一组便于数值分析的无量纲变量。 然后，我们提供了一个指向我们简单的 Python 数值代码的链接（位于 GitHub 上），该代码可用于模拟背景动力学以及膨胀期间线性扰动的演化。 该代码计算给定膨胀子势能$V(\phi)$的标量和张量功率谱。 我们讨论了使用该代码的具体算法，特别是在原始黑洞和由标量诱导的引力波背景下计算增强的标量功率谱方面。 我们还比较了文献中使用的不同变量来计算标量涨落的效率。 我们计划在未来扩展该框架，以模拟多个不同量的动力学，包括计算标量诱导的二阶张量功率谱。 显示英文摘要

摘要： Numerical simulations of the inflationary dynamics are presented here for a single canonical scalar field minimally coupled to gravity. We spell out the basic equations governing the inflationary dynamics in terms of cosmic time $t$ and define a set of dimensionless variables convenient for numerical analysis. We then provide a link to our simple numerical Python code on GitHub that can be used to simulate the background dynamics as well as the evolution of linear perturbations during inflation. The code computes both scalar and tensor power spectra for a given inflaton potential $V(\phi)$. We discuss a concrete algorithm to use the code for various purposes, especially for computing the enhanced scalar power spectrum in the context of Primordial Black Holes and scalar-induced Gravitational Waves. We also compare the efficiency of different variables used in the literature to compute the scalar fluctuations. We intend to extend the framework to simulate the dynamics of a number of different quantities, including the computation of scalar-induced second-order tensor power spectrum in the near future.