  Clusters of galaxies offer a robust test bed for probing the nature of dark
matter that is insensitive to the assumption of the gravity theories. Both
Modified Newtonian Dynamics (MOND) and General Relativity (GR) would require
similar amounts of non-baryonic matter in clusters as MOND boosts the gravity
only mildly on cluster scales. Gravitational lensing allows us to estimate the
enclosed mass in clusters on small (20 - 50 kpc) and large (several 100 kpc)
scales independent of the assumptions of equilibrium. Here we show for the
first time that a combination of strong and weak gravitational lensing effects
can set interesting limits on the phase space density of dark matter in the
centers of clusters. The phase space densities derived from lensing
observations are inconsistent with neutrino masses ranging from 2 - 7 eV, and
hence do not support the 2 eV-range particles required by MOND. To survive,
plausible modifications for MOND may be either an additional degree of
dynamical freedom in a co-variant incarnation or mass-varying theories of
neutrinos.
