Derivative interactions in de Rham-Gabadadze-Tolley massive gravity

TL;DR

This paper explores derivative interactions in de Rham-Gabadadze-Tolley massive gravity, identifying a general class of such interactions, their resummation, and the implications for ghost modes and mass scales.

Contribution

It introduces the most general derivative interactions compatible with dRGT massive gravity and analyzes their effects on the theory's consistency and ghost modes.

Findings

Infinite derivative interactions can be resummed with two parameters.

Fourth derivatives in equations imply ghosts at the cutoff scale.

Consistent derivative interactions have a mass scale much smaller than Planck mass.

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 Riemann tensor 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 fourth derivatives with respect to spacetime, which implies the appearance of ghosts at $\Lambda_3$. 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 $M_{\rm Pl}$.