paper

Derivative interactions for a spin-2 field at cubic order

arXiv:1403.6781 · doi:10.1103/PhysRevD.90.064024

Abstract

Lorentz invariant derivative interactions for a single spin-2 field are investigated, up to the cubic order. We start from the most general Lorentz invariant terms involving two spacetime derivatives, which are polynomials in the spin-2 field as well as its first derivatives. Using a perturbative Arnowitt-Deser-Misner analysis, we determined the parameters such that the corresponding Hamiltonian possesses a Lagrange multiplier, which would signify there are at most 5 degrees of freedom that are propagating. The resulting derivative terms are linear combinations of terms coming from the expansion of the Einstein-Hilbert Lagrangian around a Minkowski background, as well as the cubic "pseudolinear derivative term" identified in Hinterbichler [J. High Energy Phys. 10 (\textbf{2013}) 102]. We also derived the compatible potential terms, which are linear combinations of the expansions of the first two de Rham-Gabadadze-Tolley mass terms in unitary gauge.

18 pages, no figure; v2: Eq.(63) and comments added, published version

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