There is growing interest in using 3-dimensional neutral hydrogen mapping with the redshifted 21 cm line as a cosmological probe .
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 , focusing on the 21 cm signal from 6 < z < 20 .
We cover assumptions related to modeling of the ionization power spectrum , to the experimental specifications like array layout and detector noise , to uncertainties in the reionization history , and to the level of contamination from astrophysical foregrounds .
We derive simple analytic estimates for how various assumptions affect an experiment ’ s sensitivity , and we find that the modeling of reionization is the most important , followed by the array layout .
We present an accurate yet robust method for measuring cosmological parameters that exploits the fact that the ionization power spectra are rather smooth functions that can be accurately fit by 7 phenomenological parameters .
We find that for future experiments , marginalizing over these nuisance parameters may provide almost as tight constraints on the cosmology as if 21 cm tomography measured the matter power spectrum directly .
A future square kilometer array optimized for 21 cm tomography could improve the sensitivity to spatial curvature and neutrino masses by up to two orders of magnitude , to \Delta \Omega _ { k } \approx 0.0002 and \Delta m _ { \nu } \approx 0.007 eV , and give a 4 \sigma detection of the spectral index running predicted by the simplest inflation models .