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In previous works we proposed the Reverse Zeldovich Approximation (RZA)method, which can be used to estimate the cosmological initial conditionsunderlying the galaxy distribution in the Local Universe using peculiarvelocity data. In this paper, we apply the technique to run constrainedcosmological simulations from the RZA-reconstructed initial conditions,designed to reproduce the large-scale structure of the Local Universe. We testthe method with mock peculiar velocity catalogues extracted from a referencesimulation. We first reconstruct the initial conditions of this referencesimulation using the mock data, and then run the reconstructed initialconditions forward in time until z=0. We compare the resulting constrainedsimulations with the original simulation at z=0 to test the accuracy of thismethod. We also compare them with constrained simulations run from the mockdata without the addition of RZA, i.e. using only the currently establishedconstrained realizations (CR) method. Our re-simulations are able to correctlyrecover the evolution of the large-scale structure underlying the data. Theresults show that the addition of RZA to the CR method significantly improvesboth the reconstruction of the initial conditions and the accuracy of theobtained constrained resimulations. Haloes from the original simulation arerecovered in the re-simulations with an average accuracy of about 2 Mpc/h ontheir position and a factor of 2 in mass, down to haloes with a mass of approx10^14 M_odot/h. In comparison, without RZA the re-simulations recover only themost massive haloes with masses of about 5x10^14 M_odot/h and higher, and witha systematic shift on their position of about approx 10 Mpc/h due to the cosmicdisplacement field. We show that with the additional Lagrangian reconstructionstep introduced by the RZA, this shift can be removed.

Reconstructing cosmological initial conditions from galaxy peculiar velocities. III. Constrained simulations