Helicity decomposition of ghost-free massive gravity

Claudia De Rham, Gregory Gabadadze, Andrew J. Tolley

    Research output: Contribution to journalArticlepeer-review


    We perform a helicity decomposition in the full Lagrangian of the class of Massive Gravity theories previously proven to be free of the sixth (ghost) degree of freedom via a Hamiltonian analysis. We demonstrate, both with and without the use of nonlinear field redefinitions, that the scale at which the first interactions of the helicity-zero mode come in is Λ3 = (MPlm2)1/3, and that this is the same scale at which helicity-zero perturbation theory breaks down. We show that the number of propagating helicity modes remains five in the full nonlinear theory with sources. We clarify recent misconceptions in the literature advocating the existence of either a ghost or a breakdown of perturbation theory at the significantly lower energy scales, Λ5 = (MPlm 4)1/5 or Λ4 = (MPlm3) 1/4, which arose because relevant terms in those calculations were overlooked. As an interesting byproduct of our analysis, we show that it is possible to derive the Stückelberg formalism from the helicity decomposition, without ever invoking diffeomorphism invariance, just from a simple requirement that the kinetic terms of the helicity-two, -one and -zero modes are diagonalized.

    Original languageEnglish (US)
    Article number93
    JournalJournal of High Energy Physics
    Issue number11
    StatePublished - 2011


    • Classical theories of gravity
    • Space-time symmetries

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics


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