Testing cold dark matter models at moderate to high redshift

The Cosmic Background Explorer (COBE) microwave background temperature fluc tuations and the abundance of local rich clusters of galaxies provide the t wo most powerful constraints on cosmological models. When all variants of t he standard cold dark matter (CDM) model are subject to the combined constr aints, the power spectrum of any model is fixed to similar to 10% accuracy in both the shape and overall amplitude. These constrained models are not e xpected to differ dramatically in their local large-scale structure propert ies. However, their evolutionary histories differ, with the differences bei ng dramatically larger toward higher redshifts. In particular, it should be true that any statistical measure that probes a rapidly diminishing tail o f some distribution should provide a sensitive test at some sufficiently hi gh redshift, when the objects in question are rare and hence in the tail. W e examine in detail six standardized, COBE- and cluster-normalized CDM mode ls with respect to a large set of independent observations. The observation s include the correlation function of rich clusters of galaxies, the galaxy power spectrum, the evolution of the rich cluster abundance, the gravitati onal lensing by moderate- to high-redshift clusters, the Ly alpha forest, t he damped Ly alpha systems, the high-redshift galaxies, the reionization of the universe, and future cosmic microwave background experiments. It seems that each of the independent observations examined is potentially capable of distinguishing among at least some of the models. The combined power of several or all of these observations is tremendous. Thus, we appear to be o n the verge of being able to make dramatic tests of all the models in the n ear future using a rapidly growing set of observations, mostly at moderate to high redshift. Consistency or inconsistency among different observed phe nomena on different scales and/or at different epochs with respect to the m odels will have profound implications for the theory of the growth of cosmi c structure.