Old high-redshift galaxies and primordial density fluctuation spectra

We have discovered a population of extremely red galaxies at $z\simeq 1.5$ which have apparent stellar ages of $\gs 3$ Gyr, based on detailed spectroscopy in the rest-frame ultraviolet. In order for galaxies to have existed at the high collapse redshifts indicated by these ages, there must be a minimum level of power in the density fluctuation spectrum on galaxy scales. This paper compares the required power with that inferred from other high-redshift populations. If the collapse redshifts for the old red galaxies are in the range $z_c\simeq 6$ -- 8, there is general agreement between the various tracers on the required inhomogeneity on 1-Mpc scales. This level of small-scale power requires the Lyman-limit galaxies to be approximately $\nu\simeq 3.0$ fluctuations, implying a very large bias parameter $b\simeq 6$. The high collapse redshifts of the red galaxies as deduced from gravitational collapse provides independent support for the ages estimated from their stellar populations. Such early-forming galaxies are rare, and their contribution to the cosmological stellar density is consistent with an extrapolation to higher redshifts of the star-formation rate measured at $z<5$; there is no evidence for a general era of spheroid formation at extreme redshifts.