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We consider higher derivative corrections to the graviton three-point coupling within a weakly coupled theory of gravity. Lorentz invariance allows further structures beyond the one present in the Einstein theory. We argue that these are constrained by causality. We devise a thought experiment involving a high-energy scattering process, which leads to causality violation if the graviton three-point vertex contains the additional structures. This violation cannot be fixed by adding conventional particles with spins less than or equal to two. But, it can be fixed by adding an infinite tower of extra massive particles with higher spins. In AdS theories this implies a constraint on the conformal anomaly coefficients in terms of the dimension of the lightest single particle operator with spin greater than two. For inflation, or de Sitterlike solutions, it indicates the existence of massive higher spin particles if the gravity wave non-gaussianity deviates significantly from the one computed in the Einstein theory.

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