Annu. Rev. Astron. Astrophys. 1988. 26: 631-86
Copyright © 1988 by . All rights reserved

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In the previous sections, I described the use of rich clusters of galaxies as an efficient tracer of the large-scale structure in the Universe. In this section I summarize briefly the use of other tracers of large-scale structure: galaxies, quasars, and microwave background fluctuations. For more details, see the references listed below.

7.1. Galaxies

The study of the distribution of galaxies in space has been the classical method of surveying structure in the Universe. Redshift surveys of galaxies, covering either large areas of the sky or narrow and deep "cones," provided important information regarding the structure on scales up to ~ 20h-1 Mpc, and, more recently, to larger scales of ~ 50h-1 Mpc or more (e.g. Gregory & Thompson 1978, Tarenghi et al. 1980, Einasto et al. 1980, Chincarini et al. 1981, Gregory et al. 1981, Davis et al. 1982, Huchra et al. 1983, Oort 1983, Shanks et al. 1983, Giovanelli et al. 1986, Haynes & Giovanelli 1986, de Lapparent et al. 1986, Chincarini & Vettolani 1987, da Costa et al. 1988, Rood 1988, and references therein). While rich clusters are efficient tracers of the largest scale structure, galaxies (with their higher space density and smaller mean separation) can better trace the details of smaller and intermediate-scale structures.

The galaxy surveys reveal sharply defined structures of galaxies, frequently surrounding voids or regions underdense in galaxies. A large fraction of the galaxies appear to be located on sheetlike geometries, with occasional high-density filamentary structures such as the Perseus-Pisces supercluster (Giovanelli & Haynes 1982, Giovanelli et al. 1986, Haynes & Giovanelli 1986). The topology of the geometry may be spongy (Gott et al. 1986), i.e. exhibit connected underdense regions ("tunnels") as well as connected overdense regions. The observed voids and overdense regions range in size from a few megaparsecs to a few tens of megaparsecs. Further observations of larger and deeper samples are needed, however, before the topology can be determined more accurately.

The principal quantitative measure of the galaxy distribution used so far has been the galaxy correlation function, determined originally by Groth & Peebles (1977) from the angular distribution of galaxies in the Shane & Wirtanen (1967) counts. The galaxy correlation function is expressed by Equation 5. New observational samples yield correlations consistent with this equation (see references above; also Efstathiou 1988). It is of interest to note that while large-scale features of ~ 50h-1 Mpc or more are clearly apparent in the redshift surveys, the galaxy correlation function shows no positive correlations on scales larger than ~ 20h-1 Mpc. This is in contrast to the cluster correlation function discussed in Section 3; the latter reveals positive correlations on larger scales (gtapprox 20h-1 Mpc). Some additional statistical methods are needed that can express quantitatively the observed morphology of the galaxy distribution.

The study of the galaxy distribution can be extended to high-redshift galaxies (e.g. Koo & Kron 1987). A comparison between the clustering properties of high- and small-redshift galaxies will enable a determination of the evolution of structure with time. This information will provide important constraints on models of galaxy and structure formation.

7.2. Quasars

Quasars can provide an important tracer of structure at high redshifts. Since relatively large complete samples of quasars have recently become available, the clustering analysis of quasars has improved. Kruszewski (1986), Shaver (1984, 1988), and Zhu & Chu (1987) have analyzed the spatial distribution of quasars in different large samples. All find significant spatial correlations among quasars to large separations (~ 100h-1 Mpc). They find that quasars with z ltapprox 1.5 or 2 are very strongly correlated in space, exhibiting a correlation function that is considerably stronger than that of galaxies, comparable to the correlations of poor clusters (assuming no evolution; see Section 3). They also suggest that at z gtapprox 2 the correlations weaken considerably and are essentially undetected. Shanks et al. (1987), using a smaller sample of quasars, find strong quasar correlations at small separations (ltapprox 10h-1 Mpc) but no significant correlations on larger scales.

The strength and extent of the quasar clustering, and its dependence on redshift, will provide important clues to the understanding of large-scale structure at early times.

7.3. Microwave Background Radiation

Another tracer of the universal structure can be provided by the fluctuations in the microwave background radiation. The microwave background is observed to be isotropic to a high degree, reflecting the uniformity of the Universe over all scales at the epoch of recombination (z ~ 1000). However, if the present structure in the Universe has grown from seed fluctuations in the early Universe, then a significant level of inhomogeneity must exist in the matter (and radiation) distribution at recombination. For adiabatic models, these fluctuations are expected at the level of DeltaT / T appeq 10-4 - 10-5. Upper limits to the fluctuation amplitude have been obtained by various sensitive experiments in the range DeltaT / T = 2 × 10-5 - 3 × 10-4 on arcminute scales (Uson & Wilkinson 1984, Lasenby & Davies 1983, Readhead 1988). On large scales of a few degrees (1° corresponds to ~ 100h-1 Mpc), Davies et al (1987) have recently reported a possible detection at a level of 5 × 10-5; if these fluctuations are due to the cosmic background, they would provide evidence for cosmic large-scale structure that is considerably larger than predicted by some current models such as cold dark matter (see Section 9). Further very sensitive observations are currently underway [see, for example, Wilkinson (1988) and Lasenby (1988) for reviews] that should detect (or limit) fluctuations at a level of ~ 10-5 on various angular scales and provide a fundamental clue to the existence of structure in the very early Universe.

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