To be published in Reviews of Modern Physics

astro-ph/0406086

For a PDF version of the article, click here.

jones@astro.rug.nl

martinez@uv.es

saar@aai.ee

Physics Department, University of California, Irvine CA 92697 USA

vtrimble@astro.umd.edu

**Abstract.**
Research done during the previous century established our Standard
Cosmological Model. There are many details still to be filled in,
but few would seriously doubt the basic premise. 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 will want to describe cosmic structure quantitatively: we need to build mathematically quantifiable descriptions of 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, superclusters of galaxies 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 we are helped by making 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.
We exploit the richness of fractal scaling behavior merely as an
important supplement to the usual battery of statistical
descriptors.

We review the history of how we have learned about the structure of the Universe and present the data and methodologies that are relevant to the question of discovering and understanding 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!

**Table of Contents**

- PHYSICAL COSMOLOGY
- THE COSMIC SETTING
- EARLY IDEAS ABOUT THE GALAXY DISTRIBUTION
- Cosmogony
- Galaxies as "Island Universes"
- Earliest impressions on galaxy clustering
- Hierarchical models
- The cosmological principle
- DISCOVERING COSMIC STRUCTURE
- Early catalog builders
- Redshift Surveys
- The first generation of redshift surveys
- Recent and on-going Surveys
- The radio, X-ray and Gamma-ray skies
- Distribution of quasars and Ly-alpha clouds
- The cosmic microwave background
- MEASUREMENTS OF CLUSTERING
- The discovery of power-law clustering
- The correlation function: galaxies
- Galaxy-galaxy and cluster-cluster correlations
- The pairwise velocity dispersion
- Light does not trace mass
- FURTHER CLUSTERING MEASURES
- Higher order correlation functions
- Three-point correlation functions
- The power spectrum
- The bispectrum
- Fractal descriptors of clustering
- CLUSTERING MODELS
- Cosmological simulations
- Statistical models
- Dynamical models
- Hydrodynamic models for clustering
- Nonlinear dynamic models
- CONCLUDING REMARKS
- About scaling
- Future data gathering
- Understanding structure
- About simulations
- Where we stand on theory
- And finally ...
- REFERENCES