Causality Constraints on Corrections to the Graviton Three-Point Coupling

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 J \≤ 2. But, it can be fixed by adding an infinite tower of extra massive particles with higher spins, $J > 2$. In AdS theories this implies a constraint on the conformal anomaly coefficients \|a - c \ c \| \ 1 \ \Δgap² in terms of \Δgap, the dimension of the lightest single particle operator with spin $J > 2$. For inflation, or de Sitter-like 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.