  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 $J \leq 2$. 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 $\left|{a - c \over c} \right| \lesssim {1 \over
\Delta_{gap}^2}$ in terms of $\Delta_{gap}$, 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.
