Generalization of the Fierz-Pauli Action

Generalization of the Fierz-Pauli Action

August 13, 2010 | Claudia de Rham and Gregory Gabadadze
The paper investigates the consistency of a general covariant massive gravity theory with arbitrary polynomial interactions, focusing on the decoupling limit up to the fifth order in nonlinearities. It shows that ghost-like pathologies in the interactions of the helicity-0 mode with the helicity-2 mode can be eliminated for specific choices of the polynomial interactions. The theory is shown to be ghost-free in the decoupling limit, and the linear and some nonlinear mixing terms between the helicity-0 and -2 modes can be absorbed by a local change of variables, generating Galileon interactions. The mixing between the helicity-0 and -2 modes is at most quartic in the decoupling limit. The results suggest that the decoupling limit of the most general consistent massive gravity theory leads to Galileon interactions, which are local, preserve shift and Galilean symmetry, and have well-defined equations of motion. The paper also discusses the implications for the consistency of the effective field theory away from the decoupling limit and the Boulware-Deser problem. The findings indicate that the decoupling limit of massive gravity can be consistent up to the quintic order in interactions, and that the Galileon interactions naturally arise in this limit. The paper concludes that the decoupling limit of massive gravity is stable up to the quintic order in interactions, and that the absence of a ghost in the decoupling limit does not necessarily imply stability away from it. The paper also discusses the importance of the decoupling limit in understanding the consistency of massive gravity and the Boulware-Deser ghost.The paper investigates the consistency of a general covariant massive gravity theory with arbitrary polynomial interactions, focusing on the decoupling limit up to the fifth order in nonlinearities. It shows that ghost-like pathologies in the interactions of the helicity-0 mode with the helicity-2 mode can be eliminated for specific choices of the polynomial interactions. The theory is shown to be ghost-free in the decoupling limit, and the linear and some nonlinear mixing terms between the helicity-0 and -2 modes can be absorbed by a local change of variables, generating Galileon interactions. The mixing between the helicity-0 and -2 modes is at most quartic in the decoupling limit. The results suggest that the decoupling limit of the most general consistent massive gravity theory leads to Galileon interactions, which are local, preserve shift and Galilean symmetry, and have well-defined equations of motion. The paper also discusses the implications for the consistency of the effective field theory away from the decoupling limit and the Boulware-Deser problem. The findings indicate that the decoupling limit of massive gravity can be consistent up to the quintic order in interactions, and that the Galileon interactions naturally arise in this limit. The paper concludes that the decoupling limit of massive gravity is stable up to the quintic order in interactions, and that the absence of a ghost in the decoupling limit does not necessarily imply stability away from it. The paper also discusses the importance of the decoupling limit in understanding the consistency of massive gravity and the Boulware-Deser ghost.
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