Fractal Analysis of the UltraVISTA Galaxy Survey

TL;DR

This study applies fractal analysis to the UltraVISTA galaxy survey to investigate large-scale galaxy distribution, revealing a transition in fractal dimension at different redshift ranges, which may indicate evolving galaxy clustering or observational biases.

Contribution

Develops relativistic tools for fractal analysis of galaxy distributions and applies them to the UltraVISTA survey, extending previous work to higher redshifts and larger samples.

Findings

Fractal dimension decreases from ~1.6 to ~0.5 at higher redshifts.

Identifies two distinct redshift ranges with different fractal behaviors.

Results are consistent with previous limited surveys, suggesting possible evolutionary effects or observational biases.

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 $\Lambda$CDM cosmological model is applied to a reduced subsample in the range $0.1\le z \le 4$, and the entire sample within $0.1\le z\le 6$. Three relativistic distances are used, the luminosity distance $d_L$, redshift distance $d_z$ and galaxy area distance $d_G$, because for data at $z\gtrsim 0.3$ 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 $D=\left(1.58\pm0.20\right)$ for $z<1$, and $D=\left(0.59\pm0.28\right)$ for $1\le z\le 4$. The complete sample yielded $D=\left(1.63\pm0.20\right)$ for $z<1$ and $D=\left(0.52\pm0.29\right)$ for $1\le z\le6$. These results are consistent with those found by Conde-Saavedra et al. (2015; arXiv:1409.5409v1), 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.