Prepared for submission to JCAP The coupling to matter in Massive, Bi- and Multi-Gravity

Abstract. In this paper we construct a family of consistent ways in which matter can couple to one or more ‘metrics’/spin-2 fields in the vielbein formulation. We do so subject to requir-ing the weak equivalence principle and the absence of ghosts from pure spin-2 interactions generated by the matter action. Results are presented for Massive, Bi- and Multi-Gravity theories and we give explicit expressions for the effective matter metric in all of these cases