On Consistent Theories of Massive Spin-2 Fields Coupled to Gravity

TL;DR

This paper investigates the consistency of bimetric theories involving massive spin-2 fields coupled to gravity, identifying conditions for ghost-free interactions and the role of nonlinear fields in deviations from general relativity.

Contribution

It provides a detailed analysis of nonlinear extensions of spin-2 fields in bimetric theories, clarifies the identification of the gravitational metric, and explores ghost-free matter couplings.

Findings

Background solutions match general relativity.

Nonlinear massive field parameterizes deviations from GR.

Weak gravity limit is essential for compatibility with GR.

Abstract

We consider the issues that arise out of interpreting the ghost-free bimetric theory as a theory of a spin-2 field coupled to gravity. This requires identifying a gravitational metric and parameterizing deviations of the resulting theory from general relativity. To this end, we first consider the most general bimetric backgrounds for which a massless and a massive spin-2 fluctuation with Fierz-Pauli mass exist. These backgrounds coincide with solutions in general relativity. Based on this, we obtain nonlinear extensions of the massive and massless spin-2 fields. The background value of the nonlinear massive field parameterizes generic deviations of the bimetric theory from GR. It is also shown that the nonlinear massless field does not have standard ghost-free matter couplings, and hence cannot represent the gravitational metric. However, an appropriate gravitational metric can still be identified in the weak gravity limit. Hence in the presence of other neutral spin-2 fields, the weak gravity limit is crucial for compatibility with general relativity. We also write down the action in terms of the nonlinear massive spin-2 field and obtain its ghost-free couplings to matter. The discussion is then generalized to multimetric theories.