Analysis of Cosmological Generalized Reduced Void Probability Functions Constrained by Observations and Numerical Simulations

TL;DR

This paper combines observational survey data and numerical simulations to analyze the generalized Reduced Void Probability Function in cosmology, exploring its sensitivity to hierarchical clustering parameters and comparing results across multiple galaxy surveys.

Contribution

It introduces an optimized fit to the RVPF using GADGET-2 simulations and investigates the impact of the hierarchical reduced void parameter on void distributions in the universe.

Findings

Best parameter a near the Negative Binomial RVPF

Departure from perfect scaling over redshift range

Simulation results consistent with observational data

Abstract

Using survey data and numerical LCDM modeling we establish an optimized fit to the generalized Reduced Void Probability Function, RVPF, of Mikjian used to establish a statistical foundation to any physical process associated with hierarchical clustering. We use a numerical N-body cosmological simulation code, GADGET-2, to investigate the sensitivity of the distribution of voids characterized by the RVPF to a general hierarchical reduced void parameter, a. The void parameter is related to the Levy stability index of the distribution and Fischer critical exponent used in clustering models. We numerically simulate the evolution of the universe from a redshift of z=50 to the current epoch at z=0 in order to generate RVPFs. GADGET-2 is an N-body/smoothed particle hydrodynamics, SPH, code that we ran in MPI parallelizable mode on an HPC Beowulf cluster. The numerical data sets are compared to observational data from the Sloan digital sky Survey, SDSS, CfA, the Deep2 Galaxy Redshift Survey, and the 2dF Survey. We find the best value of the parameter a occurs near the Negative Binomial reduced void probability function but exhibits a departure from perfect scaling over the z values studied.