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 ${\mathcal{L}}_{m}=\ensuremath{-}ϵ$, where $ϵ$ is the total energy density, and the assumption that the matter fluid current is conserved [${\ensuremath{\nabla}}_{\ensuremath{\sigma}}(\ensuremath{\rho}{u}^{\ensuremath{\sigma}})=0$, where $\ensuremath{\rho}$ 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.