  We study the constraints which the next generation of radio telescopes could
place on the nature of dark energy, dark matter and inflation by studying the
gravitational lensing of high redshift 21 cm emission, and we compare with the
constraints obtainable from wide-angle surveys of galaxy lensing. If the
reionization epoch is effectively at z ~ 8 or later, very large amounts of
cosmological information will be accessible to telescopes like SKA and LOFAR.
We use simple characterizations of reionization history and of proposed
telescope designs to investigate how well the two-dimensional convergence power
spectrum, the three-dimensional matter power spectrum, the evolution of the
linear growth function, and the standard cosmological parameters can be
measured from radio data. The power spectra can be measured accurately over a
wide range of wavenumbers at z ~ 2, and the evolution in the cosmic energy
density can be probed from z ~ 0.5 to z ~ 7. This results in a characterization
of the shape of the power spectra (i.e. of the nature of dark matter and of
inflationary structure generation) which is potentially more precise than that
obtained from galaxy lensing surveys. On the other hand, the dark energy
parameters in their conventional parametrization (Omega_Lambda, w_o, w_a) are
somewhat less well constrained by feasible 21 cm lensing surveys than by an
all-sky galaxy lensing survey although a 21 cm surveys might be more powerful
than galaxy surveys for constraining models with "early" dark energy. Overall,
the best constraints come from combining surveys of the two types. This results
in extremely tight constraints on dark matter and inflation, and improves
constraints on dark energy, as judged by the standard figure of merit, by more
than an order of magnitude over either survey alone.
