A cautionary case of casual causality

Abstract

We distinguish between the notions of asymptotic causality and infrared causality for gravitational effective field theories, and show that the latter gives constraints consistent with gravitational positivity bounds. We re-explore the scattering of gravitational waves in a spherically symmetric background in the EFT of gravity in $D\ge 5$, for which the leading-order correction to Einstein gravity is determined by the Gauss-Bonnet operator. We reproduce the known result that the truncated effective theory exhibits apparent time advances relative to the background geometry for specific polarisations, which naively signal a violation of causality. We show that by properly identifying the regime of validity of the effective theory, the apparent time advance can be shown to be unresolvable. To illustrate this, we identify specific higher-dimension operators in the EFT expansion which become large for potentially resolvable time advances, rendering the EFT expansion invalid. Our results demonstrate how staying within the confines of the EFT, neither infrared nor asymptotic causality are ever violated for Einstein-Gauss-Bonnet gravity, no matter how low the scale, and furthermore its causality can be understood without appealing to a precise UV completion such as string theory.

28 pages + appendices; v2: typos corrected

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