Generalization of the Fierz-Pauli Action

TL;DR

This paper investigates the consistency of a generalized massive gravity theory, showing how specific interaction choices eliminate ghost instabilities and relate to Galileon interactions, with implications for effective field theory and the Boulware-Deser problem.

Contribution

It demonstrates that ghost-like pathologies in generalized Fierz-Pauli gravity vanish for special polynomial interactions and connects these to Galileon theories through variable redefinitions.

Findings

Ghosts disappear for special polynomial interactions.

Mixing terms can be absorbed into Galileon interactions.

Mixing between helicity-0 and -2 modes is at most quartic.

Abstract

We consider the Lagrangian of gravity covariantly amended by the mass and polynomial interaction terms with arbitrary coefficients, and reinvestigate the consistency of such a theory in the decoupling limit, up to the fifth order in the nonlinearities. We calculate explicitly the self-interactions of the helicity-0 mode, as well as the nonlinear mixing between the helicity-0 and -2 modes. We show that ghost-like pathologies in these interactions disappear for special choices of the polynomial interactions, and argue that this result remains true to all orders in the decoupling limit. Moreover, we show that the linear, and some of the nonlinear mixing terms between the helicity-0 and -2 modes can be absorbed by a local change of variables, which then naturally generates the cubic, quartic, and quintic Galileon interactions, introduced in a different context. We also point out that the mixing between the helicity-0 and 2 modes can be at most quartic in the decoupling limit. Finally, we discuss the implications of our findings for the consistency of the effective field theory away from the decoupling limit, and for the Boulware-Deser problem.