Three-dimensional mapping of dark matter

We study the prospects for three-dimensional mapping of dark matter to high redshift through the shearing of faint galaxies images at multiple distances by gravitational lensing. Such maps could provide invaluable information on the nature of the dark energy and dark matter. While in principle well posed, mapping by direct inversion introduces exceedingly large, but usefully correlated noise into the reconstruction. By carefully propagating the noise covariance, we show that lensing contains substantial information, both direct and statistical, on the large-scale radial evolution of the density field. This information can be efficiently distilled into low-order signal-to-noise eigenmodes which may be used to compress the data by over an order of magnitude. Such compression will be useful for the statistical analysis of future large data sets. The reconstructed map also contains useful information on the localization of individual massive dark matter halos, and hence the dark energy from halo number counts, but its extraction depends strongly on prior assumptions. We outline a procedure for maximum entropy and point-source regularization of the maps that can identify alternate reconstructions.