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We calculate the cubic order terms in a covariant theory that gives anonlinear completion of the Fierz-Pauli massive spin-2 action. The resultingterms have specially tuned coefficients guarantying the absence of a ghost atthis order in the decoupling limit. We show in this limit that: (1) Thequadratic theory propagates helicity-2, 1, and helicity-0 states of massivespin-2. (2) The cubic terms with six derivatives -- which would give ghosts onlocal backgrounds -- cancel out automatically. (3) There is a four-derivativecubic term for the helicity-0 field, that has been known to be ghost-free onany local background. (4) There are four-derivative cubic terms that mix twohelicity-0 fields with one helicity-2, or two helicity-1 fields with onehelicity-0; none of them give ghosts on local backgrounds. (5) In the absenceof external sources, all the cubic mixing terms can be removed by nonlinearredefinitions of the helicity-2 and helicity-1 fields. Notably, the helicity-2redefinition generates the quartic Galileon term. These findings hint to anunderlying nonlinearly realized symmetry, that should be responsible for whatappears as the accidental cancellation of the ghost.

Selftuned Massive Spin-2