Measuring the primordial deuterium abundance during the cosmic dark ages

We discuss how measurements of fluctuations in the absorption of cosmic microwave background photons by neutral gas at redshifts z approximately 7-200 could reveal the primordial deuterium abundance of the Universe. The strength of the cross-correlation of brightness-temperature fluctuations in the redshifted 21-cm line of hydrogen with those in the redshifted 92-cm line of deuterium is proportional to the value of the deuterium-to-hydrogen ratio D/H] fixed during big bang nucleosynthesis. Although challenging, this measurement would provide the cleanest possible determination of D/H], free from contamination by structure formation processes at lower redshifts. We additionally report our result for the thermal spin-change cross section in deuterium-hydrogen scattering.