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The distribution of galaxies, clusters, and pancakes that arises from the growth of primordial fluctuations is calculated. All current candidates for the gravitational mass of the universe are reviewed and classified according to the generic type of fluctuation spectrum. Particle candidates depend on the nature of the dark, weakly interacting matter which can be either "hot" (adiabatic fluctuations of massive neutrinos or baryons which dominate a low-OMEGA universe), "warm" (adiabatic fluctuations in a baryon-dominated universe with OMEGA = 1 or in a universe dominated by one of the new particles predicted by supersymmetric theories with a mass ~1 keV), or "cold" (axions or stable supersymmetric particles with mass >>1 keV, or isocurvature fluctuations in a universe dominated by baryons). We compare, for these various possibilities, a number of predictions with observations: the galaxy luminosity function, the cluster multiplicity function, and the large-scale velocity field as well as the galaxy correlations. We consider only galaxies that are primordial objects and form within a hierarchical clustering scenario, even if the initial spectrum is adiabatic and has the usual damping length. The formation of pancakes is associated with scales which are just about to turn nonlinear at the present epoch. In particular, we do not require galaxy formation to be associated with pancake collapse and fragmentation. The popular candidates for the dominant constituent of the universe can be expected to meet the requirements imposed by the various observations under conditions ranging from OMEGAh⁰. 55^> 0. 3 and an average epoch of galaxy formation ~ 5 if the fluctuation spectrum has power on all scales ("cold" dark matter) up to OMEGAh⁰. 55^> 0. 7 and ~ 1 if damping on galaxy scales was severe. This excludes only the adiabatic baryon scenario in a low-OMEGA universe, but allows massive neutrinos to produce a number of primordial galaxies that, although far too small to account for normal galaxies, could (marginally) account for the presence of quasars and rare, very luminous, galaxies at high redshift. Cold dark matter fluctuation spectra with no damping length at all may overproduce low-mass objects, whereas warm dark matter can provide a galaxy distribution that is very close to the observed galaxy counts.
Schaeffer et al. (Thu,) studied this question.