Quasi-N-body simulations, such as FastPM, provide a fast way to simulate cosmological structure formation, but have yet to adequately include the effects of massive neutrinos. We present a method to include neutrino particles in FastPM, enabling computation of the CDM and total matter power spectra to percent-level accuracy in the non-linear regime. The CDM-neutrino cross-power can also be computed at a sufficient accuracy to constrain cosmological observables. To avoid the shot noise that typically plagues neutrino particle simulations, we employ a quasi-random algorithm to sample the relevant Fermi-Dirac distribution when setting the initial neutrino thermal velocities. We additionally develop an effective distribution function to describe a set of non-degenerate neutrinos as a single particle to speed up non-degenerate simulations. The simulation is accurate for the full range of physical interest, $M_\nu \lesssim 0.6$eV, and applicable to redshifts $z\lesssim2$. Such accuracy can be achieved by initializing particles with the two-fluid approximation transfer functions (using the REPS package). Convergence can be reached in $\sim 25$ steps, with a starting redshift of $z=99$. Probing progressively smaller scales only requires an increase in the number of CDM particles being simulated, while the number of neutrino particles can remain fixed at a value less than or similar to the number of CDM particles. In turn, the percentage increase in runtime-per-step due to neutrino particles is between $\sim 5-20\%$ for runs with $1024^3$ CDM particles, and decreases as the number of CDM particles is increased. The code has been made publicly available, providing an invaluable resource to produce fast predictions for cosmological surveys.

中文翻译：

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大质量中微子非线性宇宙结构形成的快速粒子网格模拟

准 N 体模拟，例如 FastPM，提供了一种模拟宇宙结构形成的快速方法，但尚未充分包括大量中微子的影响。我们提出了一种在 FastPM 中包含中微子粒子的方法，使 CDM 和总物质功率谱的计算能够在非线性状态下达到百分比级精度。CDM-中微子交叉功率也可以以足够的精度计算，以约束宇宙学可观测量。为了避免通常困扰中微子粒子模拟的散粒噪声，我们在设置初始中微子热速度时采用准随机算法对相关的费米-狄拉克分布进行采样。我们还开发了一个有效的分布函数来将一组非简并中微子描述为单个粒子，以加速非简并模拟。该模拟对于整个物理兴趣范围是准确的，$M_\nu \lesssim 0.6$eV，并且适用于红移 $z\lesssim2$。这种精度可以通过使用二流体近似传递函数（使用 REPS 包）初始化粒子来实现。收敛可以在 $\sim 25$ 步中达到，起始红移 $z=99$。探测逐渐变小的尺度只需要增加被模拟的 CDM 粒子的数量，而中微子粒子的数量可以保持固定在一个小于或类似于 CDM 粒子数量的值。反过来，对于使用 1024^3 美元 CDM 粒子的运行，中微子粒子导致的每步运行时间增加的百分比在 $\sim 5-20\%$ 之间，并且随着 CDM 粒子数量的增加而减少。代码已经公开，