Multifractal Analysis of the Large-Scale Galaxy Distribution

This study examines the large-scale structure of the visible universe to determine if fractal scaling laws offer a plausible explanation for the distribution of galaxies. Using the extensive Updated CfA Redshift (Z) CATalog (UZCAT) compilation, which includes redshift data for around one million galaxies, we identify a reliable multifractal spectrum of the galaxy distribution on cosmological scales.

By calculating the generalized dimensions D_q and the singularity spectrum f (α), we demonstrate that the observed distribution is consistent with the weighted Cantor set model, indicative of nonlinear multifractal scaling. We find that the one-scale model parameter (p ≈ 0.45) relates to the presence of voids in the large-scale distribution of matter. Furthermore, the observed asymmetry in the spectrum may be explained by variations from the Hubble law for ideal uniform expansion

Interestingly, the overall shape of the multifractal spectrum resembles that observed by NASA's Voyager missions at the heliospheric boundaries, suggesting some universal properties of scaling across these different physical systems. However, the degree of multifractality for galaxies (Δ ≈ 0.1 – 0.17) is notably smaller than that found in heliospheric turbulence, indicating distinct underlying physical constraints despite the shared mathematical methodology.

Acknowledgments: This work has been supported by the National Science Centre, Poland (NCN), through grant No. 2021/41/B/ST10/00823.

 

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[2] W. M. Macek, A. Wawrzaszek, and L. F. Burlaga, 2014, Multifractal structures detected by Voyager 1 at the heliospheric boundaries.
Astrophys. J. Lett. 793, L30. https://doi.org/10.1088/2041-8205/793/2/L30.