Observations of the high-redshift Universe with the 21 cm hyperfine line of
neutral hydrogen promise to open an entirely new window onto the early phases
of cosmic structure formation. Here we review the physics of the 21 cm
transition, focusing on processes relevant at high redshifts, and describe the
insights to be gained from such observations. These include measuring the
matter power spectrum at z~50, observing the formation of the cosmic web and
the first luminous sources, and mapping the reionization of the intergalactic
medium. The epoch of reionization is of particular interest, because large HII
regions will seed substantial fluctuations in the 21 cm background. We also
discuss the experimental challenges involved in detecting this signal, with an
emphasis on the Galactic and extragalactic foregrounds. These increase rapidly
toward low frequencies and are especially severe for the highest redshift
applications. Assuming that these difficulties can be overcome, the redshifted
21 cm line will offer unique insight into the high-redshift Universe,
complementing other probes but providing the only direct, three-dimensional
view of structure formation from z~200 to z~6.Comment: extended review accepted by Physics Reports, 207 pages, 44 figures
(some low resolution); version with high resolution figures available at
http://pantheon.yale.edu/~srf28/21cm/index.htm; minor changes to match
published versio