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We calculate the number of damped Lyα absorbers expected in various popular cosmological models as a function of redshift and compare our predictions with observed abundances. The Press-Schechter formalism is used to obtain the distribution of halos with circular velocity in different cosmologies, and we calibrate the relation between circular velocity and absorption cross section using detailed gasdynamical simulations of a standard cold dark matter (CDM) model. Because of this calibration, our approach makes more realistic assumptions about the absorption properties of collapsed objects than previous, analytic calculations of the damped Lyα abundance. CDM models with Ω0 = 1, H0 = 50 km s-1 Mpc-1, baryon density Ωb = 0.05, and scale-invariant primeval fluctuations reproduce the observed incidence and redshift evolution of damped Lyα absorption to within observational uncertainty, for both COBE normalization (σ8 = 1.2) and a lower normalization (σ8 = 0.7) that better matches the observed cluster abundance at z = 0. A tilted (n = 0.8, σ8 = 0.7) CDM model tends to underproduce absorption, especially at z = 4. With COBE normalization, a CDM model with Ω0 = 0.4, ΩΛ = 0.6 gives an acceptable fit to the observed absorption; an open CDM model is marginally acceptable if Ω0 ≥ 0.4 and is strongly inconsistent with the z = 4 data if Ω0 = 0.3. Mixed dark matter models tend not to produce sufficient absorption, being roughly comparable to tilted CDM models if Ων = 0.2 and failing drastically if Ων = 0.3.


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