Conservation laws in theories with universal gravity/matter coupling

In this paper, we investigate the conservation laws of different types of particles in theories with a universal gravity/matter coupling. The result brings new insight about previous studies on universal gravity/matter theories. Especially, the paper demonstrates that, for perfect fluids, there is an equivalence between the assumption Lₘ=-ϵ, where $ϵ$ is the total energy density, and the assumption that the matter fluid current is conserved [∇_σ(ρu^σ)=0, where ρ is the rest mass density]. However, the main result is given in the general case in which one does not make any assumption on the conservation of the matter fluid current.