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 \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 0.35 ; ( ii ) tilted CDM models with h = 0.5 and n \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 0.75 ; ( iii ) open CDM models with h \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 0.8 and \Omega _ { 0 } \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 0.3 , and ( iv ) mixed dark matter models with h = 0.5 and \Omega _ { \nu } \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 0.2 .
Flat CDM models with a cosmological constant \lambda _ { 0 } \sim 0.7 are consistent with the observation , provided that h \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 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 .