Causality Constraints on Corrections to the Graviton Three-Point Coupling

TL;DR

This paper explores how causality constrains higher derivative corrections to the graviton three-point coupling, implying the necessity of higher spin particles for consistency in gravity theories and cosmological models.

Contribution

It establishes causality-based constraints on graviton interactions, linking them to the presence of higher spin particles and providing bounds on conformal anomaly coefficients.

Findings

Causality violation can be avoided by adding an infinite tower of higher spin particles.

Constraints on conformal anomaly coefficients relate to the gap in higher spin particle spectrum.

Implications for inflation and de Sitter models suggest higher spin particles influence gravitational non-Gaussianity.

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.