Dark Energy from Large-Scale Structure Lensing Information
  Wide area Large-Scale Structure (LSS) surveys are planning to map a
substantial fraction of the visible universe to quantify dark energy through
Baryon Acoustic Oscillations (BAO). At increasing redshift, for example that
probed by proposed 21-cm intensity mapping surveys, gravitational lensing
potentially limits the fidelity (Hui et al., 2007) because it distorts the
apparent matter distribution. In this paper we show that these distortions can
be reconstructed, and actually used to map the distribution of intervening dark
matter. The lensing information for sources at z=1-3 allows accurate
reconstruction of the gravitational potential on large scales, l <~ 100, which
is well matched for Integrated Sachs-Wolfe (ISW) effect measurements of dark
energy and its sound speed, and a strong constraint for modified gravity models
of dark energy.
  We built an optimal quadratic lensing estimator for non-Gaussian sources,
which is necessary for LSS. The phenomenon of "information saturation" (Rimes &
Hamilton, 2005) saturates reconstruction at mildly non-linear scales, where the
linear source power spectrum Delta^2 ~ 0.2-0.5. We find that steeper power
spectra, saturate more quickly. We compute the effective number densities of
independent lensing sources for LSS lensing, and find that they increase
rapidly with redshifts. For LSS/21-cm sources at z ~ 2-4, the lensing
reconstruction is limited by cosmic variance at l<~ 100.
