We calculate the number of damped Ly \alpha 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 gas dynamical 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 Ly \alpha abundance .
CDM models with \Omega _ { 0 } = 1 , H _ { 0 } = 50 km s ^ { -1 } Mpc ^ { -1 } , baryon density \Omega _ { b } = 0.05 , and scale-invariant primeval fluctuations reproduce the observed incidence and redshift evolution of damped Ly \alpha absorption to within observational uncertainty , for both COBE normalization ( \sigma _ { 8 } = 1.2 ) and a lower normalization ( \sigma _ { 8 } = 0.7 ) that better matches the observed cluster abundance at z = 0 .
A tilted ( n = 0.8 , \sigma _ { 8 } = 0.7 ) CDM model tends to underproduce absorption , especially at z = 4 .
With COBE normalization , a CDM model with \Omega _ { 0 } = 0.4 , \Omega _ { \Lambda } = 0.6 gives an acceptable fit to the observed absorption ; an open CDM model is marginally acceptable if \Omega _ { 0 } \geq 0.4 and strongly inconsistent with the z = 4 data if \Omega _ { 0 } = 0.3 .
Mixed dark matter models tend not to produce sufficient absorption , being roughly comparable to tilted CDM models if \Omega _ { \nu } = 0.2 and failing drastically if \Omega _ { \nu } = 0.3 .