  We have measured the distribution function of the flux decrement caused by
Lyman alpha forest absorption in a new sample of high resolution QSO spectra.
The observations are compared to the results from two simulations of the Lya
forest: an Eulerian Lambda-CDM model, and an SPH standard CDM model. Good
agreement between the shapes of simulated and observed distributions is
achieved by globally scaling the optical depth to match the mean flux
decrements. This procedure amounts to a measurement of the parameter Omega_b^2
h^3 / Gamma (where Omega_b is the baryonic matter density and Gamma is the HI
ionization rate). Estimating a lower limit Gamma > 7 10^{-13} s^{-1} from the
abundance of known QSOs, we derive a lower limit to the baryon density, Omega_b
h^2>0.021(0.017) for the Lambda-CDM (SCDM) model. In both cases the large
values are inconsistent with some recent D/H determinations (Rugers & Hogan
1996a,b), favoring a low deuterium abundance as reported by Tytler, Fan &
Burles (1996). Adopting a fixed Omega_b, we can determine the evolution of the
ionizing radiation field. Our models predict the intensity to be approximately
constant with redshift, consistent with the assumption that the ionizing
background is produced by known quasars for z < 3. However, additional sources
of ionizing photons are required at higher redshift.
