A Lower Bound on the Cosmic Baryon Density

We derive lower bounds on the cosmic baryon density from the requirement that the high-redshift intergalactic medium (IGM) contain enough neutral hydrogen to produce the observed Lyα absorption in quasar spectra. These analytic bounds follow from a key theoretical assumption—that absorbing structures are on average no more extended in redshift space than in real space—which is likely to hold in the gravitational instability picture of the Lyα forest, independently of the details of the cosmological model. The other ingredients that enter these bounds are an estimate of (or lower limit to) the intensity of the photoionizing UV background from quasars, a temperature T ~ 10^4 K for the "warm" photoionized IGM that produces most of the Lyα absorption, a value of the Hubble constant, and observational estimates of the mean Lyα flux decrement barD or, for a more restrictive bound, the distribution function P(τ) of Lyα optical depths. With plausible estimates of the quasar UV background and barD, the mean decrement bound implies a baryon density parameter Ω_b ~> 0.0125 h^-2, where h ≡ H_0/(100 km s^-1 Mpc^-1). A recent observational determination of P(τ) implies that Ω_b ~> 0.0125 h-2 even for a conservative estimate of the quasar UV background, and Ω_b ~> 0.018 h^-2 for a more reasonable estimate. These bounds are consistent with recent low estimates of the primordial deuterium-to-hydrogen ratio (D/H)_P, which imply that Ω_b approx 0.025 h^-2 when combined with standard big bang nucleosynthesis. Since the bounds account only for baryons in the warm IGM, their combination with the nucleosynthesis constraint implies that most of the baryons in the universe at z ~ 2-4 were distributed in diffuse intergalactic gas rather than in stars or compact dark objects. The P(τ) bound on Ω_b is incompatible with some recent high estimates of (D/H)_P, unless one drops the assumptions of standard big bang nucleosynthesis or abandons the idea that Lyα forest lines originate in the smooth, large-scale structures of photoionized gas that arise in gravitational instability theories