Small-scale power spectrum and correlations in Lambda plus cold dark matter models

Cosmological models with a positive cosmological constant (Lambda > 0) and Ohm(0) < 1 have a number of attractive features. A larger Hubble constant H-0, which can be compatible with the recent Hubble Space Telescope (HST) estimate, and a large fraction of baryon density in galaxy clusters make them current favorites. Early galaxy formation also is considered as a welcome feature of these models. But early galaxy formation implies that fluctuations on scales of a few megaparsecs spent more time in the nonlinear regime, as compared with standard cold dark matter (CDM) or cold + hot dark matter (CHDM) models. As has been known for a long time, this results in excessive clustering on small scales. We show that a typical Lambda CDM model with H-0 = 70 km s(-1) Mpc(-1), Ohm(0) = 0.3, and cosmological constant Lambda such that Omega(Lambda) = Lambda/(3H(0)(2)) = 1 - Ohm(0), 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 (sigma(8) approximate to 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 Lambda CDM models are in serious trouble, we discuss which Lambda CDM models have the best hope of surviving the confrontation with all available observational data.