Conservation laws in theories with universal gravity/matter coupling

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

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