  The radiation background produced by the 21 cm spin-flip transition of
neutral hydrogen at high redshifts can be a pristine probe of fundamental
physics and cosmology. At z~30-300, the intergalactic medium (IGM) is visible
in 21 cm absorption against the cosmic microwave background (CMB), with a
strength that depends on the thermal (and ionization) history of the IGM. Here
we examine the constraints this background can place on dark matter decay and
annihilation, which could heat and ionize the IGM through the production of
high-energy particles. Using a simple model for dark matter decay, we show
that, if the decay energy is immediately injected into the IGM, the 21 cm
background can detect energy injection rates >10^{-24} eV cm^{-3} sec^{-1}. If
all the dark matter is subject to decay, this allows us to constrain dark
matter lifetimes <10^{27} sec. Such energy injection rates are much smaller
than those typically probed by the CMB power spectra. The expected brightness
temperature fluctuations at z~50 are a fraction of a mK and can vary from the
standard calculation by up to an order of magnitude, although the difference
can be significantly smaller if some of the decay products free stream to lower
redshifts. For self-annihilating dark matter, the fluctuation amplitude can
differ by a factor <2 from the standard calculation at z~50. Note also that, in
contrast to the CMB, the 21 cm probe is sensitive to both the ionization
fraction and the IGM temperature, in principle allowing better constraints on
the decay process and heating history. We also show that strong IGM heating and
ionization can lead to an enhanced H_2 abundance, which may affect the earliest
generations of stars and galaxies.
