We reassess constraints on the cosmological baryon density from observations of the mean decrement and power spectrum of the Lyman- \alpha forest , taking into account uncertainties in all free parameters in the simplest gravitational instability model .
The uncertainty is dominated by that of the photoionizing background , but incomplete knowledge of the thermal state of the intergalactic medium also contributes significantly to the error-budget .
While current estimates of the baryon fraction from the forest do prefer values that are somewhat higher than the big bang nucleosynthesis value of \Omega _ { b } h ^ { 2 } = 0.02 \pm 0.001 , the discrepancy is at best about 3 \sigma .
For instance , assuming the highest estimate of the ionizing background , as indicated by recent measurements of a large escape fraction from Lyman-break galaxies by Steidel , Pettini & Adelberger , we find \Omega _ { b } h ^ { 2 } = 0.045 \pm 0.008 .
A recent measurement of the ionizing background from the proximity effect by Scott et al. , on the other hand , implies \Omega _ { b } h ^ { 2 } = 0.03 \pm 0.01 .
We provide an expression from which future likelihoods for \Omega _ { b } h ^ { 2 } can be derived as measurements of the ionizing background improve – consistency among constraints from the forest , nucleosynthesis and the microwave background will provide a powerful test of the gravitational instability model for the forest , and for large scale structure in general .
We also develop a formalism which treats lower bounds on the baryon density in a statistical manner , which is appropriate if only a lower bound on the ionizing background is known .
Finally , we discuss the implications of the escape fraction measurement for the age , structure and stellar content of Lyman-break galaxies .