  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 which 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. 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.
