Annu. Rev. Astron. Astrophys. 1998. 36: 599-654
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4.2. Variants of Cold Dark Matter

Based on the COBE results combined with smaller-scale constraints from galaxies, galaxy clusters, and large-scale structure, it has become apparent that there are several ways to modify the CDM model to reduce its excessive small-scale power (Efstathiou et al 1992, Wright et al 1992). These include "tilting" the primordial power spectrum index to n < 1 (TCDM), replacing some of the CDM with HDM that clusters much less efficiently on small scales (HCDM), replacing some of the CDM with a cosmological constant Lambda that does not cluster at all (LCDM), and simply eliminating most of the matter, leaving an open universe (OCDM). All these models retain the assumption of "adiabatic" primeval perturbations of the sort produced during inflation (Guth & Pi 1985). Dodelson et al (1996) have recently reviewed the status of the expanded family of CDM models.

The most obvious way to reduce small-scale power, while retaining consistency with the large-scale power required for microwave background anisotropy, is to decrease the primeval spectral index n of Equation 10, which is a possibility allowed by inflationary models. The TCDM model has been investigated with simulations by Cen et al (1992), Cen & Ostriker (1993a), Gelb et al (1993), Moscardini et al (1995). Based on their results and the more recent summaries by White et al (1995), Cole et al (1997), it appears that TCDM models with 0.7 leq n leq 0.9 remain viable, although they are less attractive than some of the other alternatives.

The HCDM model is attractive because the extra ingredient added to the CDM model is a particle that is known to exist and whose abundance is predicted in standard cosmology, the neutrino. The twist is that one or more flavors of neutrino must have nonzero masses adding up to 18.7 h2(Omeganu / 0.2) eV, where Omeganu is the fraction of the critical mass density in massive neutrinos. The first simulations of this model, performed by Davis et al (1992b), Jing et al (1993), Klypin et al (1993), showed that with Omeganu = 0.3, the HCDM model is in better agreement with observations of pairwise velocities and large-scale structure than the CDM model. Bryan et al (1994) showed that this model also succeeds in reproducing the observed abundance of X-ray clusters. However, simulations by Cen & Ostriker (1994b), Ma & Bertschinger (1994b), Klypin et al (1995) showed that galaxy formation occurs too late unless Omeganu is decreased in order to increase the small-scale power. HCDM with Omeganu = 0.2 (with one or two massive neutrino flavors) remains an attractive model, although it may overproduce rich clusters (Cen & Ostriker 1994b, Borgani et al 1997). Liddle et al (1996b) gave a recent review.

Although an astrophysically interesting cosmological constant Lambda neq 0 is very unnatural in particle physics, cosmologists are attracted by its ability to increase the age and size of the Universe for a fixed H0 as well as providing for a spatially flat model (Omegab + Omegac + OmegaLambda = 1 with OmegaLambda = Lambda / 3H02) with low matter density (Efstathiou et al 1990, Carroll et al 1992, Ostriker & Steinhardt 1995). First simulated by Davis et al (1985), this model has attracted a great deal of attention in the 1990s (e.g. Martel 1991, Suginohara & Suto 1992b, Cen et al 1993a, Cen & Ostriker 1994a, Gnedin 1996a, b). The preferred value of OmegaLambda is around 0.6-0.7, although its optimal range is still a subject of debate (e.g. Klypin et al 1996, Liddle et al 1996c).

The OCDM model with Omega = Omegab + Omegac approx 0.2 is attractive in that it requires no ingredients beyond the baryons observed and inferred from primordial nucleosynthesis and the dark matter inferred in clusters of galaxies. The case for an open universe has been presented in a review by Coles & Ellis (1994); simulations have been performed by Davis et al (1985), Martel (1991), Bahcall & Cen (1992), Kauffmann & White (1992), Cole et al (1997). Although the simplest versions of inflation favor Omega = 1 (Guth 1981), recent interest has developed among theorists in open-universe inflationary models compatible with microwave background constraints and structure formation (Liddle et al 1996a).

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