The fractal distribution of galaxies and the transition to homogeneity

Abstract

There is an ongoing debate in cosmology about the value of the length scale at which ``homogeneity'' in the matter distribution is reached or even if such a scale exists. In the wake of this debate, we intend in this letter to clarify the meaning of the statement transition to homogeneity and of the concept of correlation length. We show that there are two scales each associated to the fractal and to the homogeneous regimes of the matter distribution, respectively. The distinction between both scales has deep consequences, for there can be a regime which despite having small fluctuations around the average density exhibits large clusters of galaxies.

10 pages, 2 large PS figures, AAS macros. Substantial additions as regards the implications for cosmology, including the prospective observation of critical phenomena, and new references. Version to appear in ApJL

References in corpus (5)

• Scale-invariance of galaxy clustering
• Is the Universe Homogeneous? (On Large Scales)
• Searching for the scale of homogeneity
• Summary of Results from COBE
• The Effect of Weak Gravitational Lensing on the Cosmic Microwave Background Anisotropy: Flat versus Open Universes

Cited by in corpus (20)

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• The Scale of Cosmic Isotropy
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• The Fractal Geometry of the Cosmic Web and its Formation
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• Scale Dependent Dimension of Luminous Matter in the Universe
• The CIDA-UCM-Yale Shallow Survey for Emission Line Galaxies
• Fractal Holography: a geometric re-interpretation of cosmological large scale structure
• Fluctuations in galaxy counts: a new test for homogeneity versus fractality
• Correlation function: biasing and fractal properties of the cosmic web
• Clustering in gravitating N-body systems
• Fractal analysis of the large-scale stellar mass distribution in the Sloan Digital Sky Survey
• The exact renormalization group in Astrophysics
• Scaling laws in the stellar mass distribution and the transition to homogeneity
• Scale Symmetry in the Universe
• Fractal structures and the large scale distribution of galaxies
• Correlation Properties of Galaxies from the Main Galaxy Sample of the SDSS Survey
• Luminosity segregation versus fractal scaling in the galaxy distribution
• Complexity in Cosmology
• Phase structure of self-gravitating systems