GRAMSES：宇宙学中广义相对论$N$体模拟的新途径。部分II。初始条件
GRAMSES: a new route to general relativistic $N$-body simulations in cosmology. Part II. Initial conditions
摘要：
本文讨论了参考文献[1]中提出的非线性广义相对论（GR）$N$ -体宇宙学模拟程序GRAMSES的初始条件（IC）的生成。GRAMSES采用了一个恒定的平均曲率切片与最小的失真规范，其中的线性增长率是规模依赖的，和标准的方法来实现初始粒子数据是不直接适用的。介绍了一种新的方法，该方法与通常一样，由物质功率谱实现的位移场产生粒子的初始位置，但通过对初始红移周围的位移场进行有限差分来计算速度。通过这种方式，设置初始条件所需的所有信息都来自三个连续的输入物质功率谱，并且不需要额外的假设，例如线性增长因子和增长率的尺度无关性。我们实现了这种方法在一个修改后的2LPTic代码，并证明，在牛顿设置它可以重现速度场的默认2LPTic代码subpercent的精度。我们还表明，物质和速度的功率谱的初始粒子数据生成的GRAMSES模拟使用这种方法同意非常好的线性理论预测在特定的规范使用的GRAMSES。最后，我们讨论了辐射时的速度的有限差分计算的校正，以及在GRAMSES中实施的额外校正，以确保一致性。该方法可应用于一般规范下的GR模拟和具有尺度依赖线性增长率的宇宙学模型的模拟。
英文摘要：
We address the generation of initial conditions (ICs) for GRAMSES, a code for nonlinear general relativistic (GR) $N$-body cosmological simulations recently introduced in Ref. [1]. GRAMSES adopts a constant mean curvature slicing with a minimal distortion gauge, where the linear growth rate is scale-dependent, and the standard method for realising initial particle data is not straightforwardly applicable. A new method is introduced, in which the initial positions of particles are generated from the displacement field realised for a matter power spectrum as usual, but the velocity is calculated by finite-differencing the displacement fields around the initial redshift. In this way, all the information required for setting up the initial conditions is drawn from three consecutive input matter power spectra, and additional assumptions such as scale-independence of the linear growth factor and growth rate are not needed. We implement this method in a modified 2LPTic code, and demonstrate that in a Newtonian setting it can reproduce the velocity field given by the default 2LPTic code with subpercent accuracy. We also show that the matter and velocity power spectra of the initial particle data generated for GRAMSES simulations using this method agree very well with the linear-theory predictions in the particular gauge used by GRAMSES. Finally, we discuss corrections to the finite difference calculation of the velocity when radiation is present, as well as additional corrections implemented in GRAMSES to ensure consistency. This method can be applied in ICs generation for GR simulations in generic gauges, and simulations of cosmological models with scale-dependent linear growth rate.
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