A cautionary case of casual causality
  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.
