First galaxies that formed within halos of mass M = 10~(7.5)-10~9 solar mass at z = 30-40 in the standard cold dark matter (CDM) universe may each display an extended hydrogen 21 cm absorption halo against the cosmic microwave background, with a brightness temperature decrement of δT = -(100-150) mK at a radius 0.3 ≤ r ≤ 3.0 Mpc comoving, corresponding to an angular size of 10"-100". A 21 cm tomographic survey in the redshift shell z = 30-40 (at 35-45 MHz) is expected to encompass millions of first galaxies and may prove exceedingly profitable in enabling (at least) four fundamental applications for cosmology and galaxy formation. First, it may yield direct information on star formation physics in first galaxies. Second, it could provide a unique and sensitive probe of small-scale power in the standard cosmological model, and hence physics of dark matter and inflation. Third, it would allow for an independent, perhaps "cleaner" characterization of interesting features on large scales in the power spectrum, such as the baryonic oscillations. Finally, and possibly the most secure, each 21 cm absorption halo is expected to be highly spherical and faithfully follow the Hubble flow. By applying the Alcock-Paczynski test to a significant sample of first galaxies, one may be able to determine the dark energy equation of state with an accuracy likely only limited by the accuracy with which the matter density can be determined independently.
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