齐普夫宇宙结构定律：宇宙中最大的结构有多大？
Zipf's law for cosmic structures: how large are the greatest structures in the universe?
摘要：
宇宙中可见物质分布的统计特征是现代宇宙学的核心问题。在这方面，一个仍然缺乏明确答案的关键问题是宇宙中最大的结构有多大。这一点与这样的分布是否可以在足够大的尺度上近似为均匀分布密切相关。在这里，我们评估这个问题，考虑超星系团的大小分布和利用Zipf-Mandelbrot定律的属性，提供了一种新的方法，补充标准的分析基础上的关联函数。我们发现，星系超星系团是很好地描述了一个纯粹的齐普夫定律，没有偏差，这意味着所有的目录目前可用的是不够大，现场截断的幂律行为。这一发现提供了证据，表明当更深的红移测量完成时，预计会发现比已经观测到的最大超星系团更大的结构。因此，星系分布向均匀性过渡的尺度（如果有的话）应该相应地增加
英文摘要：
The statistical characterization of the distribution of visible matter in the universe is a central problem in modern cosmology. In this respect, a crucial question still lacking a definitive answer concerns how large are the greatest structures in the universe. This point is closely related to whether or not such a distribution can be approximated as being homogeneous on large enough scales. Here we assess this problem by considering the size distribution of superclusters of galaxies and by leveraging on the properties of Zipf-Mandelbrot law, providing a novel approach which complements standard analysis based on the correlation functions. We find that galaxy superclusters are well described by a pure Zipf's law with no deviations and this implies that all the catalogs currently available are not sufficiently large to spot a truncation in the power-law behavior. This finding provides evidence that structures larger than the greatest superclusters already observed are expected to be found when deeper redshift surveys will be completed. As a consequence the scale beyond which galaxy distribution crossovers toward homogeneity, if any, should increase accordingly
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