Abstract This paper seeks to test if the large-scale galaxy distribution can be characterized as a fractal system. Tools appropriate for describing galaxy fractal structures with a single fractal dimension D in relativistic settings are developed and applied to the UltraVISTA galaxy survey. A graph of volume-limited samples corresponding to the redshift limits in each redshift bins for absolute magnitude is presented. Fractal analysis using the standard ΛCDM cosmological model is applied to a reduced subsample in the range 0.1 ≤ z ≤ 4 , and the entire sample within 0.1 ≤ z ≤ 6 . Three relativistic distances are used, the luminosity distance d L , redshift distance d z and galaxy area distance d G , because for data at z ≳ 0.3 relativistic effects are such that for the same z these distance definitions yield different values. The results show two consecutive and distinct redshift ranges in both the reduced and complete samples where the data behave as a single fractal galaxy structure. For the reduced subsample we found that the fractal dimension is D = ( 1.58 ± 0.20 ) for z 1 , and D = ( 0.59 ± 0.28 ) for 1 ≤ z ≤ 4 . The complete sample yielded D = ( 1.63 ± 0.20 ) for z 1 and D = ( 0.52 ± 0.29 ) for 1 ≤ z ≤ 6 . These results are consistent with those found by Conde-Saavedra et al. [12] , where a similar analysis was applied to a much more limited survey at equivalent redshift depths, and suggest that either there are yet unclear observational biases causing such decrease in the fractal dimension, or the galaxy clustering was possibly more sparse and the universe void dominated in a not too distant past.

中文翻译：

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UltraVISTA 星系调查的分形分析

摘要 本文试图检验大尺度星系分布是否可以表征为一个分形系统。开发了适用于在相对论设置中描述具有单个分形维数 D 的星系分形结构的工具，并将其应用于 UltraVISTA 星系调查。呈现了与绝对量级的每个红移箱中的红移限制相对应的体积限制样本图。使用标准 ΛCDM 宇宙学模型的分形分析应用于 0.1 ≤ z ≤ 4 范围内的缩减子样本，以及 0.1 ≤ z ≤ 6 范围内的整个样本。使用了三个相对论距离，光度距离 d L 、红移距离 dz 和星系区域距离 d G ，因为对于 z ≳ 0.3 处的数据，相对论效应是这样的，对于相同的 z，这些距离定义产生不同的值。结果显示在缩减样本和完整样本中的两个连续且不同的红移范围，其中数据表现为单个分形星系结构。对于缩减的子样本，我们发现 z 1 的分形维数为 D = (1.58 ± 0.20)，1 ≤ z ≤ 4 的分形维数为 D = (0.59 ± 0.28)。完整的样本对于 z 1 产生 D = (1.63 ± 0.20)，对于 1 ≤ z ≤ 6 产生 D = (0.52 ± 0.29)。这些结果与 Conde-Saavedra 等人发现的结果一致。[12] ，其中类似的分析被应用于等效红移深度的更有限的调查，并表明要么尚不明确的观测偏差导致分形维数的这种减少，要么星系团簇可能更加稀疏并且宇宙虚空在不太遥远的过去占主导地位。