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 Tel escope (HST) estimate, and a large fraction of baryon density in galax y clusters make them current favorites. Early galaxy formation also is considered as a welcome feature of these models. But early galaxy for mation 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 kno wn for a long time, this results in excessive clustering on small scal es. 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(L ambda) = Lambda/(3H(0)(2)) = 1 - Ohm(0), normalized to COBE on large s cales and compatible with the number density of galaxy clusters, predi cts a power spectrum of galaxy clustering in real space which is too h igh: 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 de nsity produce fewer galaxies than regions with low density. Theoretica lly 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 L ambda CDM models have the best hope of surviving the confrontation wit h all available observational data.