Recovering the full velocity and density fields from large-scale redshift-distance samples

We present a new method for extracting the large-scale three-dimensional velocity and mass density fields from measurements of the radial peculiar velocities. Galaxies are assumed to trace the velocity field-not the mass. The key assumption made is that the Lagrangian velocity field has negligible vorticity, as might be expected from perturbations that grew by gravitational instability. By applying the method to cosmological N-body simulations, we demonstrate that it accurately reconstructs the velocity field. This technique promises a direct determination of the mass density field and the initial conditions for the formation of large-scale structure from galaxy peculiar velocity surveys.