Nonminimal coupling of perfect fluids to curvature

In this work, we consider different forms of relativistic perfect fluid Lagrangian densities, that yield the same gravitational field equations in General Relativity. A particularly intriguing example is the case with couplings of the form $[1+f_2(R)]{\mathcal{L}}_m$, where $R$ is the scalar curvature, which induces an extra force that depends on the form of the Lagrangian density. It has been found that, considering the Lagrangian density ${\mathcal{L}}_m=p$, where $p$ is the pressure, the extra-force vanishes. We argue that this is not the unique choice for the matter Lagrangian density, and that more natural forms for ${\mathcal{L}}_m$ do not imply the vanishing of the extra-force. Particular attention is paid to the impact on the classical equivalence between different Lagrangian descriptions of a perfect fluid.