Multifractal Analysis of Packed Swiss Cheese Cosmologies

TL;DR

This study investigates the multifractal properties of Packed Swiss Cheese cosmologies across different spatial curvatures and compares these with observational galaxy data, revealing discrepancies and potential explanations.

Contribution

It provides the first detailed multifractal analysis of PSC models in various geometries and assesses their viability against real observational data.

Findings

Space curvature does not affect the fractal spectrum.

PSC models do not match observed galaxy clustering spectra.

Luminosity biasing may explain discrepancies.

Abstract

The multifractal spectrum of various three-dimensional representations of Packed Swiss Cheese cosmologies in open, closed, and flat spaces are measured, and it is determined that the curvature of the space does not alter the associated fractal structure. These results are compared to observational data and simulated models of large scale galaxy clustering, to assess the viability of the PSC as a candidate for such structure formation. It is found that the PSC dimension spectra do not match those of observation, and possible solutions to this discrepancy are offered, including accounting for potential luminosity biasing effects. Various random and uniform sets are also analyzed to provide insight into the meaning of the multifractal spectrum as it relates to the observed scaling behaviors.