Void Statistics, Scaling, and the Origins of LargeScale Structure
Abstract
A longstanding goal in the study of largescale structure has been to discriminate reliably between various pictures of the origins of cosmological structure by objective statistical tests applied to the present state of the universe. One measure that we find to be particularly informative is the probability that a volume of given size and shape placed at random be void of galaxies. In socalled hierarchical universes, this void probability obeys a scaling relation in properly chosen variables. With such a scaling, we can obtain results that are not sensitive to artificial choices such as cutoff magnitude or sampling efficiency in the observations, or to the precise amount of dynamical evolution or the resolution of numerical simulations. We apply this probe to the observed galaxy distribution and to numerical simulations of hotparticle and coldparticle modulated inflationary models, with and without biasing isothermal or initially Poisson models, and models where structure is seeded by loops of cosmic string. In the PiscesPerseus redshift compilation of Giovanelli and Haynes, we find that the hierarchical scaling is indeed obeyed for subsamples constructed with different limiting magnitudes and subsamples taken at random. This result confirms that the hierarchical Ansatz holds valid to high order, and supports the picture that structure in the observed universe evolves by a regular process from an almost Gaussian primordial state. The simulation results obey the implied hierarchical scaling in many cases, but not in all. In particular, neutrino models without biasing show the effect of a strong feature in the initial power spectrum. Cosmic string models exhibit scaling but do not agree well with the galaxy data. Comparison of the numerical results with observations suggests that the initial fluctuation spectrum has a behavior closest to that in cold dark matter models, or perhaps Poisson.
 Publication:

The Astrophysical Journal
 Pub Date:
 May 1989
 DOI:
 10.1086/167372
 Bibcode:
 1989ApJ...340...11F
 Keywords:

 Astronomical Models;
 Computational Astrophysics;
 Galactic Clusters;
 Statistical Analysis;
 Dark Matter;
 Red Shift;
 Scaling Laws;
 Spatial Distribution;
 Astrophysics;
 COSMOLOGY;
 GALAXIES: CLUSTERING