宇宙学N体模拟的精确初始条件：截断和离散误差最小化
Accurate initial conditions for cosmological N-body simulations: Minimizing truncation and discreteness errors
摘要：
宇宙学N体模拟的初始条件的不准确很容易成为预测非线性大尺度结构的最大系统误差来源。从理论上讲，初始条件通常是由拉格朗日摄动理论的位移场的低阶截断来提供的，其中一阶和二阶近似是最常见的。在这里，我们调查所带来的改进，使用初始条件的基础上三阶拉格朗日摄动理论（3LPT）。我们表明，与3LPT，截断误差被大大抑制，从而打开门户，以初始化模拟准确地晚至z=12（我们考虑的分辨率）。我们分析了扰动截断和粒子离散对各种汇总统计量的竞争效应。离散误差本质上是衰减模式，因此对于较早的初始化时间会被强烈放大。我们表明，晚开始时间与3LPT提供最准确的配置，我们发现符合连续流体限制在1%内的功率和双谱在z=0的粒子奈奎斯特波数我们的模拟（k ~ 3 h/Mpc）。总之，为了抑制非流体伪影，我们建议使用3LPT尽可能晚地初始化模拟。我们公开了我们的3LPT初始条件生成器。
英文摘要：
Inaccuracies in the initial conditions for cosmological N-body simulations could easily be the largest source of systematic error in predicting the non-linear large-scale structure. From the theory side, initial conditions are usually provided by using low-order truncations of the displacement field from Lagrangian perturbation theory, with the first and second-order approximations being the most common ones. Here we investigate the improvement brought by using initial conditions based on third-order Lagrangian perturbation theory (3LPT). We show that with 3LPT, truncation errors are vastly suppressed, thereby opening the portal to initializing simulations accurately as late as z=12 (for the resolution we consider). We analyse the competing effects of perturbative truncation and particle discreteness on various summary statistics. Discreteness errors are essentially decaying modes and thus get strongly amplified for earlier initialization times. We show that late starting times with 3LPT provide the most accurate configuration, which we find to coincide with the continuum fluid limit within 1 per cent for the power- and bispectrum at z=0 up to the particle Nyquist wave number of our simulations (k ~ 3h/Mpc). In conclusion, to suppress non-fluid artefacts, we recommend initializing simulations as late as possible with 3LPT. We make our 3LPT initial condition generator publicly available.
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