Generalized statistical models of voids and hierarchical structure in cosmology

Abstract

Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and frequently used thermodynamic model are shown to be special cases of a more general distribution which contains a parameter "a". The parameter is related to the Levy index alpha and the Fisher critical exponent tau, the latter describing the power law fall off of clumps of matter around a phase transition. The parameter"a", exponent tau, or index alpha can be obtained from properties of a void scaling function. A stochastic probability variable "p" is introduced into a statistical model which represent the adhesive growth of galaxy structure. For p<1/2, the galaxy count distribution decays exponential fast with size. For p>1/2, an adhesive growth can go on indefinitely thereby forming an infinite supercluster. At p=1/2 a scale free power law distribution for the galaxy count distribution is present. The stochastic description also leads to consequences that have some parallels with cosmic string results, percolation theory and phase transitions.

25 pages

References in corpus (13)

• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Voids in the 2dF Galaxy Redshift Survey
• The Three-Point Correlation Function in Cosmology
• Scaling Laws in the Distribution of Galaxies
• The Evolution of Voids in the Adhesion Approximation
• Scaling in the Universe
• The 2dF Galaxy Redshift Survey: voids and hierarchical scaling models
• Monofractal Density Fluctuations and Scaling Laws for Count Probabilities and Combinants
• Bias and the power spectrum beyond the turn-over
• Scaling of voids and fractality in the galaxy distribution
• The fractal distribution of haloes
• Testing QCD Predictions for Multiplicity Distributions at HERA
• Development of particle multiplicity distributions using a general form of the grand canonical partition function and applications to L3 and H1 Data

Cited by in corpus (7)

• Angular momentum-Large-scale structure alignments in LCDM models and the SDSS
• Cosmological Systematics Beyond Nuisance Parameters : Form Filling Functions
• How to retrieve additional information from the multiplicity distributions
• Void Statistics and Hierarchical Scaling in the Halo Model
• Statistics and geometry of cosmic voids
• Void Probability Function of Simulated Surveys of high-redshift Lyman-Alpha Emitters
• Analysis of Cosmological Generalized Reduced Void Probability Functions Constrained by Observations and Numerical Simulations