Generalization of the Fierz-Pauli action

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.

Nonlinear stability of cosmological solutions in massive gravity

“…The discontinuity can be alleviated by allowing for nonlinear termsà la Vainshtein [4] but, as pointed out in 1972 by Boulware and Deser [5], generic nonlinear massive theories contain an unwanted sixth degree, in addition to the five polarizations of massive spin-2 field, which leads to ghost instability. Since then, it took a long time until a nonlinear extension of the Fierz-Pauli theory without the Boulware-Deser ghost, dubbed the dRGT theory, was found recently [6,7], where the unwanted extra degree is successfully eliminated by construction [8]. However, the absence of the sixth mode does not necessarily imply that the theory is healthy.…”

“…Ω 2 is a N × N real and symmetric matrix, which stays invariant under k → −k. The signature of the kinetic matrix is 7 We remind that in this calculation, we assumed that the second mode is a ghost, i.e. (1 − r) σ > 0.…”

“…[7]), which resides in the "normal branch". On the other hand, for the theory to have a phenomenological relevance, it is essential to obtain non-trivial background solutions which can describe the cosmological evolution.…”

On partially massless bimetric gravity

“…But they are also generically plagued by the Boulware-Deser ghost instability [12,13]. A major breakthrough in this field was the work of [14,15]. Here, the authors developed the nonlinear massive gravity for a flat reference metric f µν = η µν , the dRGT model, and established that it was ghost free in a certain "decoupling limit" analysis [16,17] that proved to be very powerful for the purpose.…”

De Sitter Galileon

“…As shown in [11,14], for a certain class of parameters, the model allows stable self-accelerating solutions. Interestingly, the Galileon family of interactions, has been shown to arise generically in other theories where gravity is mediated by a massive spin-2 field (hard mass graviton) which show no signs of the Boulware-Deser ghost in the decoupling limit [15,16,17,18].…”