Self-interactions in a model with composite gravitons

We consider a generally covariant theory of scalars minimally coupled to an auxiliary background metric, subject to the constraint of vanishing energy-momentum tensor. Eliminating the auxiliary metric leads to a non-polynomial, metric-independent action for the scalar fields. In the limit of a large number of physical scalars, a composite, massless spin-2 state, the graviton, may identified in a two-into-two scalar scattering process. We show that the emergent graviton's cubic self-interactions are consistent with those of Einstein's general relativity, up to higher-derivative corrections. We also demonstrate in a theory with more than one type of scalar that the composite graviton coupling is universal.