Constraints on the cosmic structure formation models from early formation of giant galaxies

A recent observation of Steidel and coworkers 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 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: (1) standard cold dark matter (CDM) models (where mass density Ohm(0) = 1 and power index n = 1) with the Hubble constant h less than or similar to 0.35; (2) tilted CDM models with h = 0.5 and n less than or similar to 0.75; (3) open CDM models with h less than or similar to 0.8 and Ohm(0) less than or similar to 0.3; and (4) mixed dark matter models with h = 0.5 and Ohm(v) greater than or similar to 0.2. Flat CDM models with a cosmological constant lambda(0) similar to 0.7 are consistent with the observation, provided that h greater than or similar to 0.6. Combined with constraints from large-scale structure formation, these results imply that the flat CDM model with a low Ohm(0) is the one fully consistent with observations. We predict that these high-redshift galaxies are more strongly clustered today than normal galaxies.