The low-column density Ly alpha forest

We develop an analytical method to compute the column density distribution of the Ly alpha forest in the low-column density limit. We compute the column density distributions for six different cosmological models and found that the standard, COBE-normalized CDM model cannot fit the observations of the Ly alpha forest at z = 3. The amplitude of the fluctuations in that model has to be lowered by a factor of almost 3 to match observations. However, the currently viable cosmological models like the slightly tilted COBE-normalized CDM+Lambda model, the CHDM model with Omega(nu) = 0.2, and the low-amplitude standard CDM model are all in agreement with observations for the value of the cosmological baryon density at or higher than the old standard big bang nucleosynthesis value of Omega(b)h(2) = 0.0125 for the currently favored value of the ionizing radiation intensity. With the low value for the baryon density inferred by Rugers & Hogan, the models can only marginally match observations.