On the Law of Gravity, the Mass of Neutrinos and the Proof of Dark Matter

We fit the weak lensing map of the bullet merging galaxy cluster 1E 0657-56 in a class of gravity theories interpolating between GR and MOND (General Relativity and Modified Newtonian Dynamics), so to constrain the nature and amount of dark matter with less dependence on the validity of GR on cluster scales. In agreement with Clowe et al. (2006) we show that a dominant component of non-baryonic matter is needed in the bullet cluster - in MOND as well as in GR. However, the amount of missing matter is consistent with the known inability of a purely baryonic MOND to explain dynamics of other X-ray emitting clusters. The remedy is a "marriage" of MOND with the maximum amount of existing 2eV neutrinos, also invoked in MOND fits of the CMB, which proves acceptable in all clusters. Some issues of consistency with earlier analysis of the bullet cluster are also raised