We present a novel combination of the excursion-set approach with the peak theory formalism in Lagrangian space and provide accurate predictions for halo and void statistics over a wide range of scales. The set-up is based on an effective moving barrier. Besides deriving the corresponding numerical multiplicity function, we introduce a new analytical formula reaching the percent level agreement with the exact numerical solution obtained via Monte Carlo realisations down to small scales, ∼ 10¹² h ^-1M^⊙. In the void case, we derive the dependence of the effective moving barrier on the void formation threshold, δ _v, by comparison against the Lagrangian void size function measured in the DEMNUni simulations. We discuss the mapping from Lagrangian to Eulerian space for both haloes and voids; adopting the spherical symmetry approximation, we obtain a strong agreement at intermediate and large scales. Finally, using the effective moving barrier, we derive Lagrangian void density profiles accurately matching measurements from cosmological simulations, a major achievement towards using void profiles for precision cosmology with the next generation of galaxy surveys.

中文翻译：

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通用多重性函数：计算光晕和空隙


我们提出了偏移集方法与拉格朗日空间中峰值理论形式主义的新组合，并为宽尺度上的光晕和虚空统计提供了准确的预测。该设置基于有效的移动屏障。除了推导出相应的数值多重函数外，我们还引入了一个新的解析公式，与通过蒙特卡洛实现获得的精确数值解达到百分比水平一致，具体到小尺度，∼ 10^{12 h-1}M^⊙。在空隙情况下，通过与 DEMNUni 仿真中测量的拉格朗日空隙大小函数进行比较，我们推导出了有效移动势垒对空隙形成阈值 δ_v 的依赖性。我们讨论了光晕和空隙从拉格朗日空间到欧拉空间的映射;采用球对称近似，我们在中尺度和大尺度上获得了很强的一致性。最后，利用有效的移动势垒，我们得出了拉格朗日空隙密度剖面，与宇宙学模拟的测量值精确匹配，这是在下一代星系巡天中使用空隙剖面进行精确宇宙学的重大成就。