Prospects and limitations for constraining light relics with primordial abundance measurements

The light relic density affects the thermal and expansion history of the early Universe, leaving a number of observable imprints. We focus on the primordial abundances of light elements produced during the process of big bang nucleosynthesis that are influenced by the light relic density. Primordial abundances can be used to infer the density of light relics and thereby serve as a probe of physics beyond the standard model. We calculate the observational uncertainty on primordial light element abundances and associated quantities that would be required in order for these measurements to achieve sensitivity to the light relic density comparable to that anticipated from upcoming cosmic microwave background surveys. We identify the nuclear reaction rates that need to be better measured to maximize the utility of future observations. In this work, we show that improved measurements of the primordial helium-4 abundance can improve constraints on light relics, while more precise measurements of the primordial deuterium abundance are unlikely to be competitive with cosmic microwave background measurements of the light relic density.