Generalized statistical models of voids and hierarchical structure in cosmology

TL;DR

This paper introduces a generalized statistical framework for modeling cosmic voids and hierarchical structures, linking parameters to phase transition exponents, and explores implications for galaxy growth and large-scale structure formation.

Contribution

It develops a unified model encompassing existing void and thermodynamic models, relating parameters to critical exponents and introducing a stochastic variable for galaxy growth.

Findings

The model relates void scaling to Levy and Fisher exponents.

A stochastic variable 'p' models galaxy growth, predicting exponential decay or infinite superclusters.

Power law distribution emerges at p=1/2, indicating scale-free structures.

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.