Comparing selfinteracting scalar fields and R + R 3 cosmological models

We generalize the well‐known analogies between m 2 φ 2 and R + R 2 theories to include the selfinteraction λφ 4 ‐term for the scalar field. It turns out to be the R + R 3 Lagrangian which gives an appropiate model for it. Considering a spatially flat Friedman cosmological model, common and different properties of these models are discussed, e. g., by linearizing around a ground state the masses of the resp. spin 0‐parts concide. Finally, we prove a general conformal equivalence theorem between a Lagrangian L = L ( R ), L′L ″ ≠ 0, and a minimally coupled scalar field in a general potential.