Accepted for publication in Monthly Notices of the R . A . S . Old high - redshift galaxies and primordial density fluctuation spectra

We have discovered a population of extremely red galaxies at z ≃ 1.5 which have apparent stellar ages of > ∼ 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: damped Lyman-α absorbers and Lyman-limit galaxies at z ≃ 3.2. If the collapse redshifts for the old red galaxies are in the range z c ≃ 6 – 8, there is general agreement between the various tracers on the required in-homogeneity on 1-Mpc scales. This level of small-scale power requires the Lyman-limit galaxies to be approximately ν ≃ 3.0 fluctuations, implying a very large bias parameter b ≃ 6. If the collapse redshifts of the red galaxies are indeed in the range z c = 6 − 8 required for power spectrum consistency, their implied ages at z ≃ 1.5 are between 3 and 3.8 Gyr for essentially any model universe of current age 14 Gyr. The age of these objects as deduced from gravitational collapse thus 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 extrap-olation 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.