We present the results of cosmological simulations of large-scale structure formation with massive neutrinos. The phase-space distribution of the cosmic relic neutrinos is followed, for the first time, by directly integrating the six-dimensional Vlasov-Poisson equations. Our novel approach allows us to represent free streaming and clustering of neutrinos, and their gravitational interaction with cold dark matter accurately. We thus obtain solutions for the collisionless dynamics independent of conventional N-body methods. We perform a suite of hybrid N-body/Vlasov simulations with varying the neutrino mass, and systematically examine the dynamical effects of massive neutrinos on large-scale structure formation. Our simulations show characteristic large-scale clustering of the neutrinos and their coherent streaming motions relative to dark matter. The effective local neutrino temperature around massive galaxy clusters varies by several percent with respect to the cosmic mean; the neutrinos in clusters can be hotter or colder depending on the neutrino mass. We study a number of statistics of the large-scale structure and of dark matter halos in comparison with those obtained by N-body simulations and/or by perturbation theory. Our simulations mark an important milestone in numerical cosmology, and pave a new way to study cosmic structure formation with massive neutrinos.
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