Abstract
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.
Highlights
We consider higher derivative corrections to the graviton three-point coupling within a weakly coupled theory of gravity
The constraints arise from a thought experiment where we scatter two gravitons at relatively high energy and fixed impact parameter
The energy is high compared to the inverse of the impact parameter but low compared to the scale where the theory becomes strongly coupled
Summary
In this paper we consider weakly coupled gravity theories in the tree-level approximation. This is constrained to be a linear combination of three structures, only one of which is the Einstein one These extra structures necessarily lead to a causality problem unless we introduce new higher spin particles at the scale that appears in these new three-point functions. We get stronger constraints because we are making further assumptions about the operator spectrum of the theory As another application we consider the possibility that gravity waves during inflation were generated by a theory that had these higher derivative corrections with a size comparable to the Hubble scale. We include a number of appendices to share some important but rather technical details
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