Helicity decomposition of ghost-free massive gravity

DOI10.1007/JHEP11(2011)093zbMATH Open1306.83062arXiv1108.4521OpenAlexW2093262020WikidataQ63390908 ScholiaQ63390908MaRDI QIDQ2261115

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Publication date: 6 March 2015

Published in: (Search for Journal in Brave)

Abstract: 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 $Lambd{a}_3=(M_{P}l{m}^2{)}^{1/3}$, 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, $Lambd{a}_5=(M_{P}l{m}^4{)}^{1/5}$ or $Lambd{a}_4=(M_{P}l{m}^3{)}^{1/4}$, 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 Stueckelberg 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.

Full work available at URL: https://arxiv.org/abs/1108.4521

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