Scaling laws in the distribution of galaxies

Abstract

Past surveys have revealed that the large-scale distribution of galaxies in the universe is far from random: it is highly structured over a vast range of scales. Surveys being currently undertaken and being planned for the next decades will provide a wealth of information about this structure. The ultimate goal must be not only to describe galaxy clustering as it is now, but also to explain how this arose as a consequence of evolutionary processes acting on the initial conditions that we see in the cosmic microwave background anisotropy data. In order to achieve this we need to build mathematically quantifiable descriptions of cosmic structure. Identifying where scaling laws apply and the nature of those scaling laws is an important part of understanding which physical mechanisms have been responsible for the organization of clusters of galaxies, superclusters, and the voids between them. Finding where these scaling laws are broken is equally important since this indicates the transition to different underlying physics. In describing scaling laws it is helpful to make analogies with fractals, mathematical constructs that can possess a wide variety of scaling properties. We must beware, however, of saying that the universe is a fractal on some range of scales: it merely exhibits a specific kind of fractal-like behavior on those scales. The richness of fractal scaling behavior is an important supplement to the usual battery of statistical descriptors. This article reviews the history of how we have learned about the structure of the universe and presents the data and methodologies that are relevant to an understanding of any scaling properties that structure may have. The ultimate goal is to have a complete understanding of how that structure emerged. We are getting close! CONTENTS

Fractal analysis of the dark matter and gas distributions in the Mare-Nostrum universe

“…However, χP Q is much closer to Endres & Schindelin's distance: it is also a distance and, furthermore, χ symmetrized with respect to the compared distributions, and then it diverges unless they are mutually regular. 13 The simplest example of comparison of two distributions occurs when they are both regular, in particular, when they have everywhere well-defined densities p(x) and q(x). In spite of their individual regularity, they are mutually singular if they do not overlap, that is to say, if each density is positive only where the other density vanishes, then being at Endres-Schindelin distance √ 2.…”

“…Its value has been the subject of considerable debates and still is controversial [13,14]. In contrast, the lower cutoff to scaling has attracted less attention.…”

“…Indeed, scaling laws in the distribution of galaxies have a long history, which has been reviewed in Refs. [12,13,14]. Therefore, it is interesting to compare the scaling laws in the distribution of gas with the scaling laws in the distribution of dark matter.…”

Astrophysics in 2005

“…Jones et al (2005a) concur that, while it may get better than this, it doesn't get any bigger. It would be improper to proceed without allowing Ribeiro (2005) his word.…”

Non-Gaussianity of the density distribution in accelerating universes

“…This description provides relatively accurate values even in a quasi-linear regime in the structure formation scenario [12,17,18,19,20,21,22,23,24,25,26,27,28]. (Especially, for the case of the dust fluid, this approximation is called the Zel'dovich approximation (ZA)).…”