Fractal Analysis of the UltraVISTA Galaxy Survey

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 $D=\left(1.58\pm 0.20\right)$ for $z<1$, and $D=\left(0.59\pm 0.28\right)$ for $1\le z\le 4$. The complete sample yielded $D=\left(1.63\pm 0.20\right)$ for $z<1$ and $D=\left(0.52\pm 0.29\right)$ for $1\le z\le 6$. 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.

arXiv comment9 pages, 11 figures, LaTeX. Accepted for publication in Physics Letters B

References in corpus (33)

• The Cosmic Evolution Survey (COSMOS) -- Overview
• Mass assembly in quiescent and star-forming galaxies since z=4 from UltraVISTA
• UltraVISTA: a new ultra-deep near-infrared survey in COSMOS
• The Halo Occupation Distribution and the Physics of Galaxy Formation
• Scale-invariance of galaxy clustering
• redMaGiC: Selecting Luminous Red Galaxies from the DES Science Verification Data
• Testing the Distance-Duality Relation with Galaxy Clusters and Type Ia Supernovae
• Cosmic Distance Duality Relation and the Shape of Galaxy Clusters
• Statistical Physics for Cosmic Structures
• Probing the Cosmic Distance Duality Relation with the Sunyaev-Zeldovich Effect, X-rays Observations and Supernovae Ia
• Fractal universe and cosmic acceleration in a Lemaître-Tolman-Bondi scenario
• Fractals and the Distribution of Galaxies
• Large-scale Cosmic Homogeneity from a Multifractal Analysis of the PSCz Catalogue
• On Modelling a Relativistic Hierarchical (Fractal) Cosmology by Tolman's Spacetime. I. Theory
• Multiple measurements of quasars acing as standard probes: exploring the cosmic distance duality relation at higher redshift
• Dark Energy Survey Year 1 Results: Calibration of redMaGiC Redshift Distributions in DES and SDSS from Cross-Correlations
• Fractal analysis of the galaxy distribution in the redshift range 0.45 < z < 5.0
• On Modelling a Relativistic Hierarchical (Fractal) Cosmology by Tolman's Spacetime. III. Numerical Results
• On Modelling a Relativistic Hierarchical (Fractal) Cosmology by Tolman's Spacetime. II. Analysis of the Einstein-de Sitter Model
• Halos and voids in a multifractal model of cosmic structure
• Cosmological Distances and Fractal Statistics of Galaxy Distribution
• Observations in the Einstein--de Sitter Cosmology: Dust Statistics and Limits of Apparent Homogeneity
• An interacting New Holographic Dark Energy in the framework of fractal cosmology
• Differential Density Statistics of Galaxy Distribution and the Luminosity Function
• The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies
• Scale Invariance in a Perturbed Einstein-de Sitter Cosmology
• Fractal Holography: a geometric re-interpretation of cosmological large scale structure
• Multifractal Analysis of Packed Swiss Cheese Cosmologies
• Spatial and observational homogeneities of the galaxy distribution in standard cosmologies
• The Apparent Fractal Conjecture
• Relativistic Cosmology Number Densities and the Luminosity Function
• A Dynamical Approach to a Self-similar Universe
• A model displaying extremely inhomogeneous matter distribution in General Relativity

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