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

We use our Modified Newtonian Dynamics (MOND) cosmological particle-mesh N-body code to investigate the feasibility of structure formation in a framework involving MOND and light sterile neutrinos in the mass range 11-300 eV: always assuming that Omega(nu s) = 0.225 for H-0 = 72 km s(-1) Mpc(-1). We run a suite of simulations with variants on the expansion history, cosmological variation of the MOND acceleration constant, different normalizations of the power spectrum of the initial perturbations and interpolating functions. Using various box sizes, but typically with ones of length 256 Mpc h(-1), we compare our simulated halo mass functions with observed cluster mass functions and show that (i) the sterile neutrino mass must be larger than 30 eV to account for the low-mass (M-200 < 10(14.6) M-circle dot) clusters of galaxies in MOND and (ii) regardless of sterile neutrino mass or any of the variations we mentioned above, it is not possible to form the correct number of high-mass (M-200 > 10(15.1) M-circle dot) clusters of galaxies: there is always a considerable over production. This means that the ansatz of considering the weak-field limit of MOND together with a component of light sterile neutrinos to form structure from z similar to 200 fails. If MOND is the correct description of weak-field gravitational dynamics, it could mean that subtle effects of the additional fields in covariant theories of MOND render the ansatz inaccurate, or that the gravity generated by light sterile neutrinos (or by similar hot dark matter particles) is different from that generated by the baryons.