More on effective composite metrics

In this work we study different classes of effective composite metrics proposed in the context of one-loop quantum corrections in bimetric gravity. For this purpose we consider contributions of the matter loops in form of cosmological constants and potential terms yielding two types of effective composite metrics. This guarantees a nice behaviour at the quantum level. However, the theoretical consistency at the classical level needs to be ensured additionally. It turns out that among all these possible couplings only one unique effective metric survives this criteria at the classical level.