Evolution of dispersion in the cosmic deuterium abundance

Deuterium is created during big bang nucleosynthesis, and, in contrast to the other light stable nuclei, can only be destroyed thereafter by fusion in stellar interiors. In this Letter, we study the cosmic evolution of the deuterium abundance in the interstellar medium (ISM) and its dispersion using realistic galaxy evolution models. We find that models that reproduce the observed metal abundance are compatible with observations of the deuterium abundance in the local ISM and z ~ 3 absorption line systems. In particular, we reproduce the low astration factor which we attribute to a low global star formation efficiency.We calculate the dispersion in deuterium abundance arising from different structure formation histories in different parts of the Universe. Our model also predicts a tight correlation between deuterium and metal abundances which could be used to measure the primordial deuterium abundance.