Cosmological perfect fluids in higher-order gravity

We prove that in Robertson-Walker space-times (and in generalized Robertson-Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert-Einstein Lagrangian density $F(R,\mathrm{\square }R,\mathrm{.}\mathrm{.}\mathrm{.},{\mathrm{\square }}^{k}R)$ have the form of perfect fluids in the field equations. This statement definitively allows to deal with dark energy fluids as curvature effects.