Abstract

Past surveys have revealed that the large-scale distribution of galaxies in the universe is far from random: it is highly structured over a vast range of scales. Surveys being currently undertaken and being planned for the next decades will provide a wealth of information about this structure. The ultimate goal must be not only to describe galaxy clustering as it is now, but also to explain how this arose as a consequence of evolutionary processes acting on the initial conditions that we see in the cosmic microwave background anisotropy data. In order to achieve this we need to build mathematically quantifiable descriptions of cosmic structure. Identifying where scaling laws apply and the nature of those scaling laws is an important part of understanding which physical mechanisms have been responsible for the organization of clusters of galaxies, superclusters, and the voids between them. Finding where these scaling laws are broken is equally important since this indicates the transition to different underlying physics. In describing scaling laws it is helpful to make analogies with fractals, mathematical constructs that can possess a wide variety of scaling properties. We must beware, however, of saying that the universe is a fractal on some range of scales: it merely exhibits a specific kind of fractal-like behavior on those scales. The richness of fractal scaling behavior is an important supplement to the usual battery of statistical descriptors. This article reviews the history of how we have learned about the structure of the universe and presents the data and methodologies that are relevant to an understanding of any scaling properties that structure may have. The ultimate goal is to have a complete understanding of how that structure emerged. We are getting close!

Highlights

  • Past surveys have revealed that the large-scale distribution of galaxies in the universe is far from random: it is highly structured over a vast range of scales

  • The ultimate goal must be to describe galaxy clustering as it is and to explain how this arose as a consequence of evolutionary processes acting on the initial conditions that we see in the cosmic microwave background anisotropy data

  • Most of the difficulty arises from the fact that gravitation is an always attractive force of infinite range: there is no analog to the Debye shielding in plasma physics

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Summary

Cross-disciplinary physics

Gravitation is the driving force of the cosmos, and so Einstein’s general theory of relativity is an appropriate tool for modeling the universe. That alone is not enough: other branches of physics have played a key role in building what has emerged as a “Standard Model” for cosmology. Our understanding of high-energy physics plays a key role: some have even defined a new discipline referred to as “astro-particle physics.”. There is growing evidence that the expansion of the universe is accelerating: this would require an allpervading component of matter or energy that effectively has negative pressure. If this were true we would have to resurrect Einstein’s cosmological constant or invoke some more politically correct “fifth force” concept such as quintessence

Statistical mechanics
Scaling laws in physics
Some psychological issues
THE COSMIC SETTING
Key factors
Some caveats
Cosmogony
Galaxies as “island universes”
Earliest impressions on galaxy clustering
Hierarchical models
Charlier’s hierarchy
Carpenter’s law
The cosmological principle
Early catalog builders
The Lick survey
Palomar Observatory Sky Survey
Analysis of POSS clusters
Why do this?
Redshift distortions
Flux-limited surveys and selection functions
Corrections to redshifts and magnitudes
Center for Astrophysics surveys
Southern Sky Redshift Survey and Optical Redshift Survey
IRAS redshift samples
Two-Degree Field galaxy redshift survey
Sloan Digital Sky Survey
Two-Micron All-Sky Survey and Six-Degree Field Survey
Deep spectroscopic and photometric surveys
The cosmic microwave background
Structure before our eyes
Defining the “Standard Model”
Initial conditions for galaxy formation
The discovery of power-law clustering
Definitions and scaling
Estimators
Recent determinations of the correlation function
Correlation dimension
Correlation length as a function of sample depth
Galaxy-galaxy and cluster-cluster correlations
Analysis of recent catalogs
Theoretical expectations
Richness dependence of the correlation length
The pairwise velocity dispersion
Light does not trace mass
Mass distribution and galaxy distribution: biasing
Mass and light fluctuations
Higher-order correlation functions
Three-point correlation functions
The power spectrum
The bispectrum
Fractal descriptors of clustering
A cautionary word
Structure from counts in cells
Scaling properties of counts in cells
Quantifying structure using multifractals
Intermittency
Multifractality
Aarseth
Subsequent developments
Confronting reality
Scaling in dark-matter halos
Scaling in galaxy properties
Statistical models
Neyman-Scott processes
Findings
VIII. CONCLUDING REMARKS

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