  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.
