Reconstruction of large-scale peculiar velocity fields
  A reconstruction method for recovering the initial conditions of the Universe starting from the present galaxy distribution is presented which guarantees uniqueness of solutions. We show how our method can be used to obtain the peculiar velocities of a large number of galaxies, hence trace galaxies orbits back in time and obtain the entire past dynamical history of the Universe above scales where multi-streaming has not occurred. When tested against a 128^3 LambdaCDM simulation in a box of 200 Mpc/h length, we obtain 60% exact reconstruction on scales above 6 Mpc/h. We apply our method to a real galaxy redshift catalogue, the updated NBG (Nearby Galaxies), containing 1483 galaxies, groups and clusters in a radius of 30 Mpc/h, and reconstruct the peculiar velocity fields in the local neighbourhood. Our reconstructed distances are well-matched to the observed values outside the collapsed regions if Omega_m(t)= 0.20 exp(-0.26 (t-13)) where t is the age of the Universe in Gyrs. 
Roya Mohayaee, Brent Tully and Uriel Frisch