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We use our Modified Newtonian Dynamics (MOND) cosmological particle-meshN-body code to investigate the feasibility of structure formation in aframework involving MOND and light sterile neutrinos in the mass range 11 - 300eV: always assuming that \Omega_{\nu_s}=0.225 for H_o=72 \kms Mpc^{-1}. We runa suite of simulations with variants on the expansion history, cosmologicalvariation of the MOND acceleration constant, different normalisations of thepower spectrum of the initial perturbations and interpolating functions. Usingvarious box sizes, but typically with ones of length 256 Mpc/h, we compare oursimulated halo mass functions with observed cluster mass functions and showthat (i) the sterile neutrino mass must be larger than 30 eV to account for thelow mass (M_{200}<10^{14.6} solar masses) clusters of galaxies in MOND and (ii)regardless of sterile neutrino mass or any of the variations we mentionedabove, it is not possible to form the correct number of high mass(M_{200}>10^{15.1} solar masses) clusters of galaxies: there is always aconsiderable over production. This means that the ansatz of considering theweak-field limit of MOND together with a component of light sterile neutrinosto form structure from z ~ 200 fails. If MOND is the correct description ofweak-field gravitational dynamics, it could mean that subtle effects of theadditional fields in covariant theories of MOND render the ansatz inaccurate,or that the gravity generated by light sterile neutrinos (or by similar hotdark matter particles) is different from that generated by the baryons.

Cosmological simulations in MOND: the cluster scale halo mass function with light sterile neutrinos