How accurately can 21 cm tomography constrain cosmology?

There is growing interest in using 3-dimensional neutral hydrogen mapping with the redshifted 21 cm line as a cosmological probe, as it has been argued to have a greater long-term potential than the cosmic microwave background. However, its utility depends on many assumptions. To aid experimental planning and design, we quantify how the precision with which cosmological parameters can be measured depends on a broad range of assumptions. We cover assumptions related to modeling of the ionization power spectrum and associated nonlinearity, experimental specifications like array layout and noise, cosmological assumptions about reionization history and inter-galactic medium (IGM) evolution, and assumptions about astrophysical foregrounds. We derive simple analytic approximations for how various assumptions affect the results, and find that ionization power modeling is most important, followed by array layout (crudely, the more compact, the better). We also present an accurate yet robust method for measuring cosmological parameters in practice, separating the physics from the astrophysics by exploiting both gravitationally induced clustering anisotropy and the fact that the ionization power spectra are rather smooth functions that can be accurately fit by 7 phenomenological parameters. For example, a future square kilometer array optimized for 21 cm tomography could improve the sensitivity of the Planck CMB satellite to spatial curvature and neutrino masses by up to two orders of magnitude, to Delta-Omega_k ~ 0.0002 and Delta m_nu ~ 0.007 eV, and give a 4 sigma detection of the spectral index running predicted by the simpliest inflation models.