A Functional Representation of the Cosmological Reduced Void Probability Distribution as the Fox H Function

Details A Functional Representation of the Cosmological Reduced Void Probability Distribution as the Fox H Function A Functional Representation of the Cosmological Reduced Void Probability Distribution as the Fox H Function

Jan 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aas...21560301a&link_type=abstract

American Astronomical Society, AAS Meeting #215, #603.01; Bulletin of the American Astronomical Society, Vol. 36, p.1125

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We use data from the Sloan Digital Sky Survey, the DEEP2 and 2dF Galaxy Redshift surveys and numerical runs of the Gadget II code to analyze the distribution of cosmological voids in the universe similar to the model proposed by Mekjian.1. The Void Probability Function focuses on a scaling model inspired from percolation theory that gives an analytical form for the distribution function. For large redshifts the early universe was smooth and the probability function has a simple mathematical form that mimics the two point correlation results leading to a generalized power law. As various large scale galactic structures emerge in a given simulation a number of relatively empty regions are isolated and characterized as voids based upon number counts in the associated volume. The number density of these regions is such that the universe has a large scale “sponge-like” appearance with voids of all scales permeating the field of observation. For these data sets we examine the range of critical void probability function parameters that give rise to the best fit to the numerical and observational data. Several expressions for the probability distribution differ at the long end tail of the distribution which is sensitive to the Levy index of the distribution. Almost all of the distributions can be expressed as special cases of the Fox H function which has an asymptotic form whose tail depends upon the Levy index. We analyze the Levy index expressions and link them to the Fox H function parameters and to an anomalous diffusion equation that gives rise to the observed LSS void pattern.
We wish to thank the Kentucky Space Grant Consortium for providing the NASA grant funding this research
1. Aram Z. Mekjian , Generalized statistical models of voids and hierarchical structure in cosmology, The Astrophysical Journal, 655: 1-10, 2007, arXiv:0712.1217

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