Constraints on the Cosmic Structure Formation Models from Early Formation of Giant Galaxies

A recent observation of Steidel et al. indicates that a substantial fraction of giant galaxies were formed at an epoch as early as redshift $z>3-3.5$. We show that this early formation of giant galaxies gives strong constraints on models of cosmic structure formation. Adopting the COBE normalization for the density perturbation spectrum, we argue that the following models do not have large enough power on galactic scales to yield the observed abundance: (i) standard cold dark matter (CDM) models (where mass density $\Omega_0=1$ and power index $n=1$) with the Hubble constant $h\lsim 0.35$; (ii) tilted CDM models with $h=0.5$ and $n\lsim 0.75$; (iii) open CDM models with $h\lsim 0.8$ and $\Omega_0 \lsim 0.3$, and (iv) mixed dark matter models with $h=0.5$ and $\Omega _\nu \gsim 0.2$. Flat CDM models with a cosmological constant $\lambda_0 \sim 0.7$ are consistent with the observation, provided that $h\gsim 0.6$. Combined with constraints from large-scale structure formation, these results imply that the flat CDM model with a low $\Omega_0$ is the only one that is fully consistent with observations. We predict that these high-redshift galaxies are more strongly clustered than normal galaxies observed today.