Review: Multifractal Analysis of Packed Swiss Cheese Cosmologies

  title={Review: Multifractal Analysis of Packed Swiss Cheese Cosmologies},
  author={Jonas Mureika and Charles C. Dyer},
  journal={General Relativity and Gravitation},
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… 
Fractality in cosmic topology models with spectral action gravity
We consider cosmological models based on the spectral action formulation of (modified) gravity. We analyze the coupled effects, in this model, of the presence of nontrivial cosmic topology and of
Bell Polynomials and Brownian Bridge in Spectral Gravity Models on Multifractal Robertson–Walker Cosmologies
We obtain an explicit formula for the full expansion of the spectral action on Robertson–Walker spacetimes, expressed in terms of Bell polynomials, using Brownian bridge integrals and the Feynman–Kac
Nonlinear effects of general relativity from multiscale structure
When do the nonlinear effects of general relativity matter in astrophysical situations? They are obviously relevant for very compact sources of the gravitational field, such as neutron stars or black
Slowly decaying waves on spherically symmetric spacetimes and ultracompact neutron stars
We prove that, in a class of spherically symmetric spacetimes exhibiting stable trapping of null geodesics, linear waves cannot (uniformly) decay faster than logarithmically. When these linear waves
Variations on Birkhoff’s theorem
The relation between the expanding universe and local vacuum solutions, such as that for the Solar System, is crucially mediated by Birkhoff’s theorem. Here we consider how that relation works, and
Texture analysis using lacunarity and average local variance
This work compared four multi-scale texture metrics accessible in the spatial domain (lacunarity, average local variance (ALV), and two novel variations) in terms of ease of interpretation, sensitivity and computational cost, and analyzed a variety of patterns and textures.


Multifractal analysis of the galaxy distribution: Reliability of results from finite data sets.
It is found that the presently available galaxy samples can be usefully employed to trace the scaling properties generated by nonlinear clustering, and the different methods display different advantages and pitfalls.
On Fractal Modeling in Astrophysics: The Effect of Lacunarity on the Convergence of Algorithms for Scaling Exponents.
Fractals and multifractals are used to model hierarchical, inhomogeneous structures in several areas of astrophysics, notably the distribution of matter at various scales in the universe. Current
Multifractal properties of cosmological N-body simulations
We study the multifractal properties of cosmological N-body simulations. The integrations have been carried out for a cold dark matter spectrum and for two scale-free spectra with spectral indices
Galaxy number counts and fractal correlations
We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each other and manifest fractal correlations (with dimension D 2) up to the
Clustering paradigms and multifractal measures
A subsample of the CfA galaxy catalog and two clustering models look different to the eye, yet have comparable two-point correlation functions. It is shown how the technique of measure analysis
Clustering statistics in cosmology
The main tools in cosmology for comparing theoretical models with the observations of the galaxy distribution are statistical. We will review the applications of spatial statistics to the description
The Spatial correlation function of RICH clusters of galaxies
A series of objective statistical estimators is applied to directly study the three-dimensional distribution of rich clusters, using a recently completed redshift sample of 104 Abell clusters out to
On modeling a relativistic hierarchical (fractal) cosmology by Tolman's spacetime. II - Analysis of the Einstein-de Sitter model
This paper studies the spatially homogeneous Einstein-de Sitter cosmological model in the context of a relativistic hierarchical (fractal) cosmology as developed in the first paper in this series. We
Angular projections of fractal sets
We discuss various questions which arise when one considers the central projection of three-dimensional fractal sets (galaxy catalogs) onto the celestial globe. The issues are related to how fractal
The Las Campanas Redshift Survey
The Las Campanas Redshift Survey (LCRS) consists of 26418 redshifts of galaxies selected from a CCD-based catalog obtained in the $R$ band. The survey covers over 700 square degrees in 6 strips, each