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 $$ left|frac{a-c}{c}right|lesssim frac{1}{delta_{mathrm{gap}}^2} $$ n terms of δgap, the dimension of the lightest single trace 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.