The coupling to matter in Massive, Bi- and Multi-Gravity

TL;DR

This paper explores various consistent methods of coupling matter to multiple spin-2 fields in massive, bi-, and multi-gravity theories, ensuring the weak equivalence principle and ghost-free interactions.

Contribution

It introduces new coupling schemes for matter in multi-gravity theories that satisfy key physical and consistency conditions.

Findings

Explicit matter coupling expressions for all considered theories

Demonstration of ghost-free matter interactions

Preservation of the weak equivalence principle

Abstract

In this paper we construct a family of ways in which matter can couple to one or more `metrics'/spin-2 fields in the vielbein formulation. We do so subject to requiring 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.