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9. The cluster mass function

In the CDM model rich clusters of galaxies grow out of the rare peak upward fluctuations in the primeval Gaussian mass distribution. Within this model one can adjust the amplitude of the mass fluctuations to match the abundance of clusters at one epoch. In the Einstein-de Sitter model it is difficult to see how this one free adjustment can account for the abundance of rich clusters now and at redshifts near unity. (85)

Most authors now agree that the low density flat LambdaCDM model can give a reasonable fit to the cluster abundances as a function of redshift. The constraint on OmegaM0 from the present cluster abundance still is under discussion, but generally is found to be close to OmegaM0 ~ 0.3 if galaxies trace mass. (86) The constraint from the evolution of the cluster number density also is under discussion. (87) The predicted evolution is slower in a lower density universe, and at given OmegaM0 the evolution is slower in an open model with Lambda = 0 than in a spatially-flat model with Lambda (for the reasons discussed in Sec. III.D). Bahcall and Fan (1998) emphasize that we have good evidence for the presence of some massive clusters at z ~ 1, and that this is exceedingly difficult to understand in the CDM model in the Einstein-de Sitter cosmology (when biasing is adjusted to get a reasonable present number density). Low density models with or without Lambda can account for the existence of some massive clusters at high redshift. Distinguishing between the predictions of the spatially curved and flat low density cases awaits better measurements.



85 Early discussions of this problem include Evrard (1989), Peebles, Daly, and Juszkiewicz (1989), and Oukbir and Blanchard (1992). Back.

86 For recent discussions see Pierpaoli, Scott, and White (2001), Seljak (2001), Viana, Nichol, and Liddle (2002), Ikebe et al. (2002), Bahcall et al. (2002), and references therein. Wang and Steinhardt (1998) and Lokas and Hoffman (2001) consider this test in the context of the XCDM parametrization; to our knowledge it has not been studied in the scalar field dark energy case. Back.

87 Examples include Blanchard et al. (2000), and Borgani et al. (2001). Back.

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