Scaling in the Universe

Abstract

The aim of this review article is to give a comprehensive description of the scaling properties detected for the distribution of cosmic structures. Due to the great variety of statistical methods to describe the large-scale structure of the Universe, I will mainly concentrate on those methods which reveal remarkable regularities and scaling in the structure of the Universe. Although in most cases I prefer not to enter into the technical aspects of how implementing such methods, more details will be furnishes about the description of galaxy clustering in terms of fractal concepts. Despite recent claims for a Universe, which behaves like a fractal at arbitrarily large scales, I will show that the fractal language can be usefully employed to disprove this picture. The emerging scenario is that of a Universe, which behaves like a self-similar structure at small scales, where fractality is dynamically generated by non-linear gravitational clustering, while preserving large-scale homogeneity. Nevertheless, even at scales $\magcir 10\hm$, where gravity still acts linearly, the distribution of galaxy clusters shows remarkable scale-invariant features, which could give precise hints about the initial conditions for the evolution of the large-scale structure of the Universe.

165 pages plus 44 figures available on request to [email protected], uuencoded compressed postscript file, Physycs Reports (in press)

References in corpus (10)

• The Cold Dark Matter Density Perturbation
• Biasing and Hierarchical Statistics in Large-scale Structure
• Structure Formation with Cold + Hot Dark Matter
• Moments of the Counts Distribution in the 1.2 Jy IRAS Redshift Survey
• Nonlinear evolution of density perturbations using approximate constancy of gravitational potential
• The Mass Function of Nearby Galaxy Clusters
• Higher Order Moments of the Matter Distribution in Scale--Free Cosmological Simulations with Large Dynamic Range
• Large-Scale Clustering in Bubble Models
• Angular Distribution of Clustersin Skewed CDM Models
• Large--Scale Angular Correlations in CDM Models

Cited by in corpus (42)

• The density and peculiar velocity fields of nearby galaxies
• The WiggleZ Dark Energy Survey: the transition to large-scale cosmic homogeneity
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• X-ray Clusters of Galaxies as Tracers of Structure in the Universe
• Fractal Dimension as a measure of the scale of Homogeneity
• Scaling Laws in the Distribution of Galaxies
• The scale of homogeneity of the galaxy distribution in SDSS DR6
• Testing homogeneity on large scales in the Sloan Digital Sky Survey Data Release One
• The Scale of Cosmic Isotropy
• Fractal Dimensions of a Weakly Clustered Distribution and the Scale of Homogeneity
• Analysing Large Scale Structure: I. Weighted Scaling Indices and Constrained Randomisation
• Polarized anisotropic spectral distortions of the CMB: Galactic and extragalactic constraints on photon-axion conversion
• Testing homogeneity in the Sloan Digital Sky Survey Data Release Twelve with Shannon entropy
• A method for testing the cosmic homogeneity with Shannon entropy
• The Fractal Geometry of the Cosmic Web and its Formation
• Constructing, characterizing, and simulating Gaussian and higher-order point distributions
• The Fractal Universe
• An information theory based search for homogeneity on the largest accessible scale
• Clustering of Local Extrema in Planck CMB maps
• Superclustering with the Atacama Cosmology Telescope and Dark Energy Survey: I. Evidence for thermal energy anisotropy using oriented stacking
• Probing large scale homogeneity and periodicity in the LRG distribution using Shannon entropy
• X-ray spectroscopy in the microcalorimeter era II: A new Diagnostic on Column Density from the Case A to B Transition in H- and He-like Iron
• Clustering of loose groups and galaxies from the Perseus--Pisces Survey
• Correlation function: biasing and fractal properties of the cosmic web
• Conditional Cumulants in Weakly Non-linear Regime
• Boundary Corrections in Fractal Analysis of Galaxy Surveys
• Statistics and geometry of cosmic voids
• Fractal analysis of the large-scale stellar mass distribution in the Sloan Digital Sky Survey
• Fractal distributions of dark matter and gas in the MareNostrum Universe
• Are galaxy distributions scale invariant? A perspective from dynamical systems theory
• Generalized statistical models of voids and hierarchical structure in cosmology
• Extension Of Bertrand's Theorem And Factorization Of The Radial Schrödinger Equation
• Studying neutral hydrogen structures during the epoch of reionization using fractal dimensions
• Testing homogeneity of the galaxy distribution in the SDSS using Renyi entropy
• The maximum extent of the filaments and sheets in the cosmic web: an analysis of the SDSS DR17
• Scaling Regimes in the Distribution of Galaxies
• Magnetoresistive study of antiferromagnetic--weak ferromagnetic transition in single-crystal La${}_2$CuO${}_{4+\delta }$
• Scaling laws in the stellar mass distribution and the transition to homogeneity
• Scale Symmetry in the Universe
• Information of Structures in Galaxy Distribution
• Morpho-statistical characterisation of the spatial galaxy distribution through Gibbs point processes
• Time evolution of the mutual information between disjoint regions in the Universe