超越TopHat滤波器的物质一点概率分布函数
One-point matter PDFs beyond TopHat filters
中文总结 AI 辅助
该研究构建了球对称窗函数下物质密度的一点PDF解析模型，开发了计算领头阶球坍缩部分的数值管道，经N体模拟验证，可描述大尺度结构，且欠密区剖面具通用性，过密区则随滤波器变化，对EFT修正敏感度一致。
中文摘要 AI 辅助
我们研究了采用任意球对称窗函数平均后的物质密度的一点概率分布函数（PDF）。该PDF在路径积分框架内进行解析建模，能够对大尺度结构进行非微扰描述。它包含由球对称引力坍缩动力学控制的领头阶贡献，以及由非球对称涨落产生的一阶因子。我们开发了一个数值管道，用于计算PDF的领头阶球坍缩部分，并将其应用于坐标空间中在TopHat滤波器和高斯滤波器之间插值的一系列窗函数，以及具有非单调径向依赖的窗函数。我们发现，当对滤波器宽度进行归一化以产生固定的线性平均密度方差时，PDF对滤波器的选择弱依赖。对于每个滤波器和每个平均密度值，我们的管道会给出最概然密度剖面。我们发现，在过密区域，这些剖面对于不同滤波器差异很大，但在欠密区域则紧密遵循通用曲线。我们获得了在小密度对比度下有效的PDF非球对称部分的微扰表达式，从中发现，无论滤波器边界的平滑程度如何，所有PDF对描述小尺度成团的有效场论（EFT）修正的敏感度相同。我们将PDF模型与高分辨率N体模拟的结果进行了测试，对于宽度大于10 Mpc/h的滤波器，一致性极佳；对于较窄的滤波器，出现了百分之几的小偏差，这被解释为高阶微扰修正。
英文摘要
We study the one-point probability distribution function (PDF) for matter densities averaged with an arbitrary spherically symmetric window function. The PDF is analytically modeled within the path integral framework, enabling a non-perturbative description of large-scale structure. It contains a leading order contribution controlled by the spherically symmetric gravitational collapse dynamics, as well as an order-one factor arising from aspherical fluctuations. We develop a numerical pipeline to compute the leading spherical-collapse part of the PDF and apply it to a family of window functions interpolating between the TopHat and Gaussian filters in coordinate space, as well as to a window function with non-monotonic radial dependence. We find that the PDF weakly depends on the choice of the filter, provided the width of the filter is normalized to yield a fixed linear averaged density variance. For each filter and each value of the averaged density, our pipeline gives the most probable density profile. We find that these profiles vastly differ for different filters in the case of overdensities, but closely follow a universal curve at underdensities. We obtain a perturbative expression for the aspherical part of the PDF valid at small density contrasts. We find from it that all PDFs are equally sensitive to the effective field theory (EFT) corrections accounting for short-scale clustering, regardless of how smooth the filter's boundary is. We test our PDF model against the results of high-resolution N-body simulations. The agreement is excellent for filters with widths larger than 10 Mpc/h. Small discrepancies at a few percent level arise for narrower filters and are interpreted as higher-order perturbative corrections.
