Large Scale Structure in Universes Dominated by Cold Dark Matter

Abstract

The theory of the peaks of Gaussian random density fields is applied to a numerological study of the large scale structure from adiabatic fluctuations expected in models of biased galaxy formation in Ω = 1, h = 0.5 universes dominated by cold dark matter (CDM). The number density of rich clusters is sensitive to model assumptions but can plausibly bracket the observed number. The amplitude of the rich cluster correlation function is too small for r > 20 h ^-1 Mpc and generally has the wrong shape. The angular anisotropy of the cross-correlation function ξ_cl,g demonstrates that the far field regions of cluster-scale peaks are asymmetric as recent observations indicate. These regions will generate pancakes or filaments upon collapse. One-dimensional singularities in the large-scale bulk flow should arise in these CDM models, appearing as pancakes in position space. They are too rare to explain the CfA bubble walls, but pancakes that are just turning around now are sufficiently abundant and would appear to be thin walls normal to the line of sight in redshift space. Large-scale streaming velocities on ~ 30 h ^-1 Mpc scales are significantly smaller than recent observations indicate. To explain the reported ~ 700 km s ^-1 coherent motions, mass must be significantly more, clustered than galaxies with a biasing factor b < 0.4 and a nonlinear redshift z _nl at cluster scales > 1 for both massive neutrino and cold models. With biasing and CDM, b ~ 2 and clusters are rare events.