Small-Scale Power Spectrum and Correlations in Lambda + Cold Dark Matter Models

Cosmological models with a positive cosmological constant (LAMBDA > 0) and OMEGA₀_ LAMBDA_ = LAMBDA/ (3H₀_²^) = 1 - OMEGA₀_, normalized to COBE on large scales and compatible with the number density of galaxy clusters, predicts a power spectrum of galaxy clustering in real space which is too high: at least twice larger than CfA estimates and 3 times larger than estimates for the APM Galaxy Survey for wavenumbers k = (0. 4- 1) h Mpc^-1^. This conclusion holds if we assume either that galaxies trace the dark matter (σ₈_ ~ 1. 1 for this model) or just that a region with higher density produces more galaxies than a region with lower density. The only way to reconcile the model with the observed power spectrum P (k) is to assume that regions with high dark matter density produce fewer galaxies than regions with low density. Theoretically this is possible, but it seems very unlikely: X-ray emission from groups and clusters indicates that places with a large density of dark matter produce a large number of galaxies. Since it follows that the low-OMEGA LAMBDACDM models are in serious trouble, we discuss which ACDM models have the best hope of surviving the confrontation with all available observational data.