Any viable cosmological model must produce enough structure at early epochs to explain the amount of gas associated with high-redshift damped Ly \alpha systems .
We study the evolution of damped Ly \alpha systems at redshifts z \geq 2 in cold dark matter ( CDM ) and cold+hot dark matter ( CDM+HDM ) models using both N -body and hydrodynamic simulations .
Our approach incorporates the effects of gas dynamics , and we find that all earlier estimates which assumed that all the baryons in dark matter halos would contribute to damped Ly \alpha absorption have overestimated the column density distribution f ( N ) and the fraction of neutral dense gas \Omega _ { g } in damped Ly \alpha systems .
The differences are driven by ionization of hydrogen in the outskirts of galactic halos and by gaseous dissipation near the halo centers , and they tend to exacerbate the problem of late galaxy formation in CDM+HDM models .
We only include systems up to the highest observed column density N \sim 10 ^ { 21.8 } cm ^ { -2 } in the estimation of \Omega _ { g } for a fair comparison with data .
If the observed f ( N ) and \Omega _ { g } inferred from a small number of confirmed and candidate absorbers are robust , the amount of gas in damped Ly \alpha systems at high redshifts in the \Omega _ { \nu } = 0.2 CDM+HDM model falls well below the observations .