• DOI:10.1007/JHEP05(2013)086
• Corpus ID: 118612069

On consistent theories of massive spin-2 fields coupled to gravity

@article{Hassan2012OnCT,
  title={On consistent theories of massive spin-2 fields coupled to gravity},
  author={Sayed Fawad Hassan and Angnis Schmidt-May and Mikael von Strauss},
  journal={Journal of High Energy Physics},
  year={2012},
  volume={2013},
  pages={1-32}
}

• Sayed Fawad Hassan, A. Schmidt-May, M. V. Strauss
• Published 7 August 2012
• Physics, Geology
• Journal of High Energy Physics

A bstractWe 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 exist, and we compute the most general expression for the Fierz-Pauli mass. 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 most natural 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.