Prospects for precision cosmology with the 21 cm signal from the dark ages

The 21 cm signal from the dark ages provides a potential new probe of fundamental cosmology. While exotic physics could be discovered, here we quantify the expected benefits within the standard cosmology. A measurement of the global (sky-averaged) 21 cm signal to the precision of thermal noise from a 1,000 h integration would yield a measurement within 10% of a combination of cosmological parameters. A 10,000 h integration would improve this measurement to 3.2% and constrain the cosmic helium fraction to 9.9%. Precision cosmology with 21 cm fluctuations requires a collecting area of 10 km$^2$ (corresponding to 400,000 stations), which, with a 1,000 h integration, would exceed the same global case by a factor of $\sim2$. Enhancing the collecting area or integration time by an order of magnitude would yield a 0.5% parameter combination, a helium measurement five times better than Planck and a constraint on the neutrino mass as good as Planck. Our analysis sets a baseline for upcoming lunar and space-based dark-ages experiments.