Annu. Rev. Astron. Astrophys. 1993. 31: 689-716
Copyright © 1993 by . All rights reserved

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Before turning to an overall assessment of the CDM model, it may be useful to mention some of the variations on the classic version of this theory. As the difficulties for the latter have mounted, many of the original promulgators of that picture have added other elements to the scenario, enabling a better fit with the developing observations.

4.1 New Directions

While the scale-free n = 1 spectrum usually adopted is intuitively plausible and is consistent with the COBE finding of n = 1.1 ± 0.6, several authors have pointed out that variants with "tilted" spectra n < 1 are in fact more likely, as a detailed consequence of specific theories for inflation. Lucchin & Mataresse (1985), Vittorio et al (1988), Steinhardt (1991), Adams et al (1993), Salopek et al (1989), and recently Cen et al (1992, other references to earlier work contained therein) propose and explore such tilted models. In general, a spectral index n = 0.7-0.8 is plausible in terms of fundamental physics and provides a much better fit to large-scale structure observations and to the small-scale velocity field than does the classic n = 1 version of the theory. However, this tilt (for fixed large-scale COBE normalization) lowers the small-scale power, making galaxy formation still later than it is in standard CDM. In addition, for n neq 1, gravitational waves may produce CBR fluctuations, thereby lowering sigma8 for a given COBE measurement. As an example, for the tilted model n = 0.8, Lucchin et al (1992) compute that sigma8 will be lowered by a factor of 1.4 (see also Davis et al 1992). Thus, the gain comes at a cost which may not be supportable.

An opposite set of virtues and defects is possessed by the models relying on non-Gaussian perturbations such as textures (e.g. Gooding et al 1991, Cen et al 1991, Salopek 1992). Since small parts of the universe are always in a nonlinear state in this model, early galaxy and quasar formation is assured. However, the dynamical aspect of developing textures produces additional CBR fluctuations which again lowers the normalization sigma8 by a significant factor (after matching to COBE). The model so normalized may then have difficulty in achieving the large-scale coherent velocity field observed in galaxies and clusters.

The open but flat variant championed by Efstathiou (1992, see also Turner et al 1984, Peebles 1984, Blumenthal et al 1988, Vittorio & Silk 1992) in which Omegah = 0.3, Omega approx 0.2, and Lambda = 0.8 is very attractive on many grounds but may have a similar defect. It matches the large-scale structure observations very well and also the small-scale velocity field. But the large value and coherence of the large-scale velocity field may constitute a severe difficulty. Among the most attractive aspects of this picture is that, since Omega < 1 at recent epochs, the late over-merging of galaxies will be mitigated. As in all open models, galaxy formation is earlier - another considerable advantage. Combinations of the last two options, such as open, tilted models, have also been proposed (Vittorio et al 1988, Tormen et al 1992).

Lastly, there is the "mixed dark matter" model (Davis et al 1992, Holtzman & Primack 1993, Gelb et al 1992), which maintains Omega = 1 but reduces the small-scale power relative to large-scale power by adding dark neutrinos to the mix. Once again, large-scale and small-scale structures can be matched to observations. Both the large-scale and small-scale velocity fields can also be fit. But galaxy formation is late and one returns to the classic question in such a model: Why do the bulk of the dynamical observations indicate that Omega is small when both types of dark matter should be measured in clusters of galaxies?

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