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We compute, including a current state-of-the-art treatment of hydrodynamical processes, heating, and cooling, a variety of cosmological models into the extreme nonlinear phase to enable comparisons with observations. First, we note the common, model-independent results. All have a mean (z = 0) temperature of 104.5 - 105.5 K, set essentially by photoheating processes. Most gas is in one of two components: either at the photoheating floor 104.5 K and primarily in low-density regions, or else shock heated to 105-106 K and in regions of moderate overdensity (in caustics and near groups and clusters). It presents a major challenge to observationally detect this second, abundant component, since it is neither an efficient radiator nor an efficient absorber. About 2%-1O% of the baryons cool and collapse into galaxies forming on caustics and migrating to clusters. About 1%-2% of baryons are in the very hot X-ray-emitting gas near cluster cores, in good agreement with observations. These correspondences between the simulations and the real world imply that there is some significant truth to the underlying standard scenarios for the growth of structure. The differences among model predictions may help us find the path to the correct model. For COBE-normalized models, the most relevant differences concern epoch of structure formation. In the open variants having Ω = 0.3, with or without a cosmological constant, structure formation on galactic scales is well advanced at redshift z = 5, and reionization occurs early. But if observations require models for which most galaxy formation occurs more recently than z = 2, then the flat Ω = 1 models are to be preferred. The velocity dispersion on the 1 h-1 Mpc scale also provides a strong discriminant with, as expected, the ω = 1 models giving a much higher (perhaps too high) value for that statistic.
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