We have discovered a population of extremely red galaxies at z similar or equal to 1.5 which have apparent stellar ages of greater than or similar to 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 Ly alpha absorbers and Lyman-limit galaxies at z similar or equal to 3.2., If the collapse redshifts for the old red galaxies are in the range z(c) similar or equal to 6-8, there is general agreement between the various tracers on the required inhomogeneity on l-Mpc scales. This level of small-scale power requires the Lyman-limit galaxies to be approximately nu similar or equal to 3.0 fluctuations, implying a very large bias parameter b similar or equal to 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 similar or equal to 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 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.