The Cosmological Baryon Density from the Deuterium Abundance at a redshift z = 3.57

We present a measurement of the deuterium to hydrogen ratio in a quasar absorption system at redshift z = 3.57 towards QSO 1937-1009. We use a two component fit, with redshifts determined from unsaturated metal lines, to fit the hydrogen and deuterium features simultaneously. We find a low value of D/H = 2.3 \pm 0.6 \times 10^{-5}, which does not agree with other measurements of high D/H (Songaila et al. 1994, Carswell et al. 1994). The absorption system is very metal poor, with metallicities less than 1/100 solar. Standard models of chemical evolution show the astration of deuterium is limited to a few percent from primordial for systems this metal-poor, so we believe our value represents the primordial one. Using predictions of standard big-bang nucleosynthesis and measurements of the cosmic microwave background, our measurement gives the density of baryons in units of the critical density, $\Omega_b h^2 = 0.024 \pm 0.006$, where $H_0 = 100 h km s^{-1] Mpc^{-1}$.