Dark matter gravity force is generated by the expansion of the universe, gravitational force is not strong enough and an extra centripetal force is needed due to this expansion, energy related to this new force is stored in the dark matter energy tensor D(4,0) related to the Riemann curvature. The cosmological redshift energy loss due to the expansion of the universe is stored in the dark matter energy tensor D(4,0). The Cosmic Microwave Background energy loss has been stored in the dark matter energy tensor D(4,0) Dark matter gravity is generated by D(4,0) energy related directly to the S(4,0) tensor, however this gravity is attributed to exotic particles never detected, galaxies in our universe are rotating with such speed that the gravity generated by their observable matter could not possibly hold them together Total Energy T(4,0) and energy tensors are defined to complete the General Relativity field equations. The Ricci decomposition is a way of breaking up the Riemann curvature tensor into three orthogonal tensors, Z(4,0), Weyl tensor C(4,0) and S(4,0)