Measuring the Primordial Deuterium Abundance During the Cosmic Dark Ages

We discuss how measurements of fluctuations in the absorption of cosmic microwave background (CMB) photons by neutral gas during the cosmic dark ages, at redshifts z ~ 7--200, could reveal the primordial deuterium abundance of the Universe. The strength of the cross-correlation of brightness-temperature fluctuations due to resonant absorption of CMB photons in the 21-cm line of neutral hydrogen with those due to resonant absorption of CMB photons in the 92-cm line of neutral deuterium is proportional to the fossil deuterium to hydrogen ratio [D/H] fixed during big bang nucleosynthesis (BBN). Although technically challenging, this measurement could provide the cleanest possible determination of [D/H], free from contamination by structure formation processes at lower redshifts, and has the potential to improve BBN constraints to the baryon density of the Universe \Omega_{b} h^2. We also present our results for the thermal spin-change cross-section for deuterium-hydrogen scattering, which may be useful in a more general context than we describe here.