加权网络：形态学信息标记场
Weighted Webs: Morphology-Informed Marked Fields
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中文总结 AI 辅助
研究宇宙网形态编码的高阶宇宙学信息，通过标记功率谱框架，探讨对局部环境形态敏感的标记，研究多种标记函数，量化其对关键宇宙学参数的约束，发现结合不同标记可增强约束，为相关研究提供框架。
中文摘要 AI 辅助
晚期物质分布形成的宇宙网形态编码了超越标准两点统计所包含的宇宙学信息。标记功率谱通过研究由局部环境密度函数“标记”（即加权）的密度场的两点统计，提供了一个计算高效的框架来获取此高阶信息。在这项工作中，我们探索对局部环境形态敏感而非仅对其密度敏感的标记的潜力。我们研究了广泛的此类标记，考虑基于平滑密度、潮汐切变幅度、局部各向同性和丝状度、这些量的高斯变换以及局部分形维数估计器的标记函数。我们根据不同标记对关键宇宙学参数的约束来量化其优点，包括物质丰度$\Omega_m$、涨落幅度$\sigma_8$和中微子质量$M_\nu$。我们发现依赖密度的标记继续比标准功率谱提供最大的改进，而基于形态的标记自身改进较小。然而，结合基于密度和形态的标记始终能增强宇宙学约束，超出任何一类单独实现的效果，表明它们探测了底层物质分布的互补方面。这些结果对基于形态的标记统计进行了系统评估，并探索了宇宙网的哪些几何属性对宇宙学参数推断最有效。它们还为未来对最优标记及其与高阶相关函数的微扰联系的研究建立了一个基于物理的框架。
英文摘要
The morphology of the cosmic web formed by the late-time matter distribution encodes cosmological information beyond that contained in standard two-point statistics. Marked power spectra provide a computationally efficient framework to access this higher-order information, by studying the two-point statistics of the density field ``marked'' (i.e. weighted) by a function of its local environmental density. In this work we explore the potential of marks that are sensitive to the morphology of this local environment, rather than simply its density. We study a broad range of such marks, considering mark functions based on the smoothed density, tidal shear amplitude, local degree of isotropy and filamentarity, Gaussian transformations of these quantities and a local fractal dimension estimator. We quantify the merit of different marks in terms of their constraints on key cosmological parameters, including the matter abundance $Ω_m$, the amplitude of fluctuations $σ_8$, and the mass of neutrinos $M_ν$. We have found that density-dependent marks continue to provide the largest improvements over the standard power spectrum, while morphology-based marks yield more modest improvements on their own. Nevertheless, combining density- and morphology-based marks consistently enhances cosmological constraints beyond what either class achieves separately, demonstrating that they probe complementary aspects of the underlying matter distribution. These results provide a systematic assessment of morphology-based marked statistics and explore which geometric properties of the cosmic web contribute most effectively to cosmological parameter inference. They also establish a physically motivated framework for future investigations of optimal marks and their perturbative connection to higher-order correlation functions.
