We present a new Particle-Mesh cosmological N-body code for accurately solving the modified Poisson equation of the Quasi Linear formulation of MOND. We generate initial conditions for the Angus (2009) cosmological model, which is identical to LCDM except that the cold dark matter is switched for a single species of thermal sterile neutrinos. We set the initial conditions at z=250 for a (512 Mpc/h)^3 box with 256^3 particles and we evolve them down to z=0. We clearly demonstrate the necessity of MOND for developing the large scale structure in a hot dark matter cosmology and contradict the naive expectation that MOND cannot form galaxy clusters. We find that the correct order of magnitude of X-ray clusters (with T_X > 4.5 keV) can be formed, but that we overpredict the number of very rich clusters and seriously underpredict the number of lower mass clusters. The latter is a shortcoming of the resolution of our simulations, whereas we suggest that the over production of very rich clusters might be prevented by incorporating a MOND acceleration constant that varies with redshift and an expansion history that cannot be described by the usual Friedmann models. We present evidence that suggests the density profiles of our simulated clusters are compatible with those of observed X-ray clusters in MOND. It remains to be seen if the low mass end of the cluster mass function can be reproduced and if the high densities of dark matter in the central 20 kpc of groups and clusters of galaxies, measured in the MOND framework, can be achieved. As a last test, we computed the relative velocity between pairs of halos within 10 Mpc and find that pairs with velocities larger than 3000 km/s like the bullet cluster, can form without difficulty.Comment: 9 pages, 7 figur
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