Generalization of the Fierz-Pauli action

By Claudia de Rham, G. Gabadadze. 2010

1,061 citations recorded by the source corpus.

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 ghostlike 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d532dba2fbf494afc825c3c1534bcf63ff8abb14

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Citations in the corpus

On non-linear actions for massive gravity (2011, methodology): “Thus, while the candidate ghost-free actions considered in [ 6 , 7] and here are a step forward, the final question of non-linear massive gravity is far from settled.”
New positivity bounds from full crossing symmetry (2020, background): “B(s;t) ˘ g2 D 4 x 4 + y 6 + x2 8 + ; (4.5) again neglecting order unity factors. Galileon theories are scalar eld theory that captures salient features of a number of massive gravitational models [45,46,64,65] but have also been considered in their own right as eective theories with soft behaviour”
Interacting spin-2 fields (2012, methodology): “For the case of a single interacting massive graviton, this problem was solved only recently, by the dRGT (de Rham, Gabadadze, Tolley) massive gravity theories described in [2, 3].”
Bimetric gravity is cosmologically viable (2015, background): “[7] Claudia de Rham and Gregory Gabadadze, “Generalization of the Fierz-Pauli Action,” Phys.”
Beyond the Cosmological Standard Model (2014, positive): “Although galileons originally arose in brane-world modifications of gravity, they have appeared in other well-behaved modifications of gravity, for instance massive gravity [217, 218].”