Cosmological Information in the Gravitational Lensing of Pregalactic HI
  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. 
R. Benton Metcalf and S.D.M. White