  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.
