What is the right way to interpret a massive graviton? We generalize the kinematical framework of general relativity to multiple connections. The average of the connections is itself a connection and plays the role of the canonical connection in standard general relativity. At the level of dynamics, the simplest choice of the Einstein-Hilbert action is indistinguishable from the single-connection case. However, inspired by Weyl geometry, we show how one can construct massive gravity to all orders in perturbation theory compatible with the de Rham-Gabadadze-Tolley ghost-free model. We conclude that the mass of the graviton can be interpreted as a geometrical property of spacetime arising from two connections. Furthermore, in the multiconnection framework there is no ambiguity in the definition of the physical metric and consequently coupling to matter.

• Received 17 September 2013

DOI:https://doi.org/10.1103/PhysRevD.89.024004