Testing Cold Dark Matter Models At Moderate to High Redshift

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Abstract
(shortened) This paper consists of three parts. In the first part, we develop and test an analytic method to compute mass and auto-correlation functions of rich clusters of galaxies based on the formalism of Gaussian peaks. In the second part, we apply this method to constrain all variants of the Gaussian cold dark matter (CDM) cosmological model using the observed abundance of local rich clusters of galaxies and the microwave background temperature fluctuations observed by COBE. The combined constraint (i.e., when both COBE and cluster normalized) fixes the power spectrum of any model to about 10% accuracy in both shape and overall amplitude, resulting in six representative models. In the last part, we examine in detail all the COBE and cluster normalized models with respect to a large set of independent observations. Observations include cluster correlation function, galaxy power spectrum, evolution of rich cluster abundance, gravitational lensing by moderate-to-high redshift clusters of galaxies, Lyman alpha forest, high redshift galaxies, damped Lyman alpha systems, reionization of the universe and future CMB experiments. It seems that each of the independent observations examined is potentially capable of distinguishing between at least some of the models. The combined power of several or all of these observations is tremendous. Thus, we appear to be on the verge of being able to make dramatic tests of all models in the near future using a rapidly growing set of observations, mostly at moderate to high redshift. Consistency or inconsistency between different observed phenomena on different scales and/or at different epochs with respect to the models will have profound implications for the theory of growth of cosmic structure.

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