大尺度结构一维和三维功率谱响应：倒塌后动力学公式的检验
Power spectrum response of large-scale structure in 1D and in 3D: tests of prescriptions for post-collapse dynamics
摘要：
宇宙大尺度结构的功率谱响应函数描述了演化的功率谱如何通过引力演化的非线性模式耦合由初始功率的微小变化来修改。以前发现，从小到大尺度的耦合的响应函数在振幅上被强烈抑制，特别是在后期，与基于单流近似的微扰理论（PT）的预测相比。一个明显的解释是，PT未能描述壳层穿越之外的动力学。我们测试这个想法比较测量$N$体模拟处方PT的基础上，但增加了自适应平滑，以考虑在多流制度的各种大小的非线性结构的形成。我们首先从一维（1D）宇宙学开始，其中泽尔多维奇近似提供了单流状态的精确解。与三维情况类似，大尺度模式的响应函数在小尺度下表现出很强的振幅抑制，这不能单独用Zel'dovich解来解释。然而，通过执行自适应平滑的初始条件，以确定不同大小的晕，并解决近似后崩溃的3流制度的动态，理论和模拟之间的协议大大提高。我们将我们的分析扩展到3D的情况下，使用PINOCCHIO算法，其中类似的自适应平滑实现拉格朗日PT字段，以识别晕，并结合一个球形晕处方，以考虑崩溃后的动态。再次，抑制被发现在小规模和大规模模式之间的耦合和模拟的协议得到改善。
英文摘要：
The power spectrum response function of the large-scale structure of the Universe describes how the evolved power spectrum is modified by a small change in initial power through non-linear mode coupling of gravitational evolution. It was previously found that the response function for the coupling from small to large scales is strongly suppressed in amplitude, especially at late times, compared to predictions from perturbation theory (PT) based on the single-stream approximation. One obvious explanation for this is that PT fails to describe the dynamics beyond shell-crossing. We test this idea by comparing measurements in $N$-body simulations to prescriptions based on PT but augmented with adaptive smoothing to account for the formation of non-linear structures of various sizes in the multi-stream regime. We first start with one-dimensional (1D) cosmology, where the Zel'dovich approximation provides the exact solution in the single stream regime. Similarly to the 3D case, the response function of the large-scale modes exhibits a strong suppression in amplitude at small scales which cannot be explained by the Zel'dovich solution alone. However, by performing adaptive smoothing of initial conditions to identify haloes of different sizes and solving approximately post-collapse dynamics in the 3-streams regime, agreement between theory and simulations drastically improves. We extend our analyses to the 3D case using PINOCCHIO algorithm, in which similar adaptive smoothing is implemented on the Lagrangian PT fields to identify haloes and is combined with a spherical halo prescription to account for post-collapse dynamics. Again, a suppression is found in the coupling between small- and large-scale modes and the agreement with simulations is improved.
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