### Abstract

We investigate the possibility of a new massive gravity theory with derivative interactions as an extension of de Rham-Gabadadze-Tolley massive gravity. We find the most general Lagrangian of derivative interactions using a Riemann tensor whose cutoff energy scale is Λ_{3}, which is consistent with de Rham-Gabadadze-Tolley massive gravity. Surprisingly, this infinite number of derivative interactions can be resummed with the same method in de Rham-Gabadadze-Tolley massive gravity, and remaining interactions contain only two parameters. We show that the equations of motion for scalar and tensor modes in the decoupling limit contain fourth derivatives with respect to spacetime, which implies the appearance of ghosts at Λ_{3}. We claim that consistent derivative interactions in de Rham-Gabadadze-Tolley massive gravity have a mass scale M, which is much smaller than the Planck mass M_{Pl}.

Original language | English |
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Article number | 084025 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 88 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2013 Oct 16 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*88*(8), [084025]. https://doi.org/10.1103/PhysRevD.88.084025