The large-scale smoothness of the Universe

Abstract

The Universe is inhomogeneousÐand essentially fractalÐon the scale of galaxies and clusters of galaxies, but most cosmologists believe that on larger scales it becomes isotropic and homogeneous: this is the`cosmological principle'. This principle was ®rst adopted when observational cosmology was in its infancy, and was then little more than a conjecture. The data now available offer a quantitative picture of the gradual transition from small-scale fractal behaviour to large-scale homogeneity.A fractal is a distribution or shape that is not homogeneous (in general), but possesses the property that each part is a simulacrum of the whole. In other words it`looks' the same on all scales. Fractals abound in nature: for example, the coastline of a small peninsula drawn on paper could equally well depict a large continent; and fractals have long been studied as manifestations of scaling laws in solid-state physics 1,2 . The clustering of galaxies (see Fig. 1) lends itself to a fractal description 1±7 , because the clumpiness prevails over a wide range of scales. The big question for cosmology is whether the distribution of matter continues to be a simple fractal beyond the scale of clusters of galaxies: if it does, then the cosmological principle is invalid.Past attempts to determine the distribution of matter have confronted two important obstacles. Most of the mass in the Universe is dark; we can detect it only by its gravitational effect on objects that we can see, and it is still unclear how to relate the distributions of light and mass. In particular, we have not known how to match the clustering of galaxies with the cosmic microwave background (CMB) anisotropies, which tell us about the mass uctuations in the early Universe. In addition, little has been known about¯uctuations in the distribution of matter on scales intermediate between those of local galaxy surveys (( 100 h -1 Mpc, where h is the Hubble constant in units of 100 km s -1 Mpc -1 ) and scales probed by the Cosmic Background Explorer (COBE) satellite () 1,000 h -1 Mpc).Recent observations of radio galaxies and the X-ray background (XRB, which probably arises from distant active galactic nuclei), at median redshift Å z < 1, can now effectively probe these intermediate scales.Moreover, experiments to measure¯uctuations in the microwave background on smaller angular scales than those probed by COBE are also helping to bridge the gap. Future surveys of more than one million galaxies will probe to a median redshift Å z < 0:1 (which roughly corresponds to a co-moving distance of ,300 h -1 Mpc). Current data, however, already strongly constrain any non-uniformities in the galaxy distribution (as well as the overall mass distribution) on scales ) 300 h -1 Mpc.In the language of fractals (see Box 1), fractal dimensions are used to characterize the degree of clustering: these generalize our intuitive concepts of dimension and can take any positive value less than or equal to 3. On scales below ,10 h -1 Mpc, galaxies are distributed with the correlation dimension...

Cosmological Tests from the New Surveys

“…One can use this estimate to derive the fractal dimension D 2 of the universe on large scales. Although the fractal dimension of the galaxy distribution on scales < 20h −1 Mpc is D 2 ≈ 1.2 − 2.2, the fluctuations in the X-ray Background and in the Cosmic Microwave Background are consistent with D 2 = 3 to within 10 −4 on the very large scales (Wu et al 1998).…”

Large-scale variations of the cosmic X-ray background and the X-ray emissivity of the local Universe

“…Wu et al 1999). Due to this uniformity and because most of the CXB originates at relatively large distances from us (at redshifts z ∼ 1−2, e.g.…”

Fractal structures and the large scale distribution of galaxies

“…We do not enter here in the details of the discussion about real data (see e.g. Joyce et al 1999, Wu et al 1999, however in the last section we consider separately the case (i) λ 0 ≈ 50h −1 M pc, (ii) λ 0 ≈ 300h −1 M pc and (iii) λ 0 ≈ 1000h −1 M pc, briefly discussing the main theoretical consequences.…”

“…While in the first case one is able to have a clear and unambiguous answer from the data, in the second one is only able to make some weaker claims about the compatibility of the data with a fractal or a homogeneous distribution. For example the papers of Wu et al 49 and Nusser & Lahav 36 mainly concern with compatibility arguments, rather than with direct tests. However, also in this second case, it is possible to understand some important properties of the data, and to clarify the role and the limits of some underlying assumptions which are often used without a critical perspective.…”

“…Nowadays there is a general agreement about the fact that galactic structures are fractal up to a distance scale of ∼ 50h −1 M pc 46,30 and the increasing interest about the fractal versus homogeneous distribution of galaxy in the last year 10,42,49,6,34,28,7,32,36 has focused, mainly on the determination of the homogeneity scale λ 0 . b The main point in this discussion is that galaxy structures are fractal no matter what is the crossover scale, and this fact has never been properly appreciated.…”