  Cosmological models with a positive cosmological constant and $\Omega_0<1$
have a number of attractive features. A larger Hubble constant, which can be
compatible with the recent 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 few megaparsec scales spent more time in the
nonlinearregime, as compared with standard Cold Dark Matter (CDM) or Cold+Hot
Dark Matter models. This results in excessive clustering on small scales. We
show that a typical LCDM model with $H_0=70$ km/s/Mpc, $\Omega_0=0.3$
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: {\it at least} twice larger than CfA estimates (Park \etal
1994) and 3 times larger than APM estimates (Baugh \& Efstathiou 1994) for
wavenumbers $k=(0.4-1)h/{\rm Mpc}$. This conclusion holds if we assume either
that galaxies trace the dark matter ($\sigma_8\approx 1.1$ 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 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- $\Omega$ LCDM models are in serious trouble, we
discuss which LCDM models have the best hope of surviving the confrontation
with available observational data.
