标题： 原初黑洞的小规模聚集：云中云和排斥效应 显示英文标题

标题： Small-scale clustering of Primordial Black Holes: cloud-in-cloud and exclusion effects

摘要： 使用一种轨迹集方法，我们重新研究了原初黑洞（PBHs）在早期宇宙中由于大尺度高斯密度涨落的哈勃重入而产生的初始空间聚集。 我们推导了PBHs的两点相关函数，并正确考虑了“云中云”机制。 我们的表达式自然且内在地关联了PBH对的形成，这是与聚类的泊松模型的一个关键区别。 我们的方法有效包含了短程排斥效应，并阐明了小尺度上的聚类行为：PBHs在短距离上呈反相关。 使用与尺度无关的坍缩阈值，我们推导了在距离$r$处找到PBH对的超额概率，以及找到质量比不对称的PBH对的超额概率。 我们的框架在构造上是模型无关的，我们讨论了可能的其他应用。 显示英文摘要

摘要： Using an excursion-set approach, we revisit the initial spatial clustering of Primordial Black Holes (PBHs) originating from the Hubble re-entry of large Gaussian density fluctuations in the early universe. We derive the two-point correlation functions of PBHs, properly accounting for the "cloud-in-cloud" mechanism. Our expressions naturally and intrinsically correlate the formation of pairs of PBHs, which is a key difference with the Poisson model of clustering. Our approach effectively includes short-range exclusion effects and clarifies the clustering behaviors at small scale: PBHs are anti-correlated at short distances. Using a scale-independent collapse threshold, we derive explicit expressions for the excess probability to find pairs of PBHs separated by a distance $r$, as well as the excess probability to find pairs with asymmetric mass ratio. Our framework is model-independent by construction and we discuss possible other applications.