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 ≤ 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.
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Camanho, X.O., Edelstein, J.D., Maldacena, J. et al. Causality constraints on corrections to the graviton three-point coupling. J. High Energ. Phys. 2016, 20 (2016). https://doi.org/10.1007/JHEP02(2016)020
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DOI: https://doi.org/10.1007/JHEP02(2016)020