Rampei Kimura, Daisuke Yamauchi
We investigate a possibility of new massive gravity theory with derivative interactions as an extension of de Rham-Gabadadze-Tolley massive gravity. We found the most general Lagrangian of derivative interactions whose cutoff energy scale is $\Lambda_3$, 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 4th derivative with respect to space-time, which implies the appearance of ghosts at $\Lambda_3$. We claim that consistent derivative interactions in de Rham-Gabadadze-Tolley massive gravity has a mass scale $M$, which is much smaller than the Planck mass $M_{\rm Pl}$.
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http://arxiv.org/abs/1308.0523
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