Causality in Curved Spacetimes: The Speed of Light & Gravity
Claudia de Rham, Andrew J. Tolley
TL;DR
The paper analyzes causality, analyticity, and causality constraints in curved spacetimes for low-energy EFTs of QED and gravity. It develops a framework based on refractive-index concepts, Eisenbud–Wigner time delays, and gravitational TT amplitudes to study how small superluminal corrections arise without violating causality within the EFT’s regime of validity, a mechanism termed self-protection. It shows that resolvable macroscopic time advances do not occur in consistent gravity or QED EFTs, even when low-energy speeds are mildly superluminal, and clarifies the role of the decoupling limit in diagnosing frame-dependent causality. The results have implications for constraining cosmological and gravitational EFTs, guiding how causality tests should be applied to curved backgrounds and highlighting when analyticity allows or forbids certain superluminal behaviors. Overall, the work emphasizes that causality in curved spacetimes is preserved by limiting the EFT’s regime of validity and distinguishing resolvable from unresolvable time advances, with frame and UV-completion considerations playing a crucial role.
Abstract
Within the low-energy effective field theories of QED and gravity, the low-energy speed of light or that of gravitational waves can typically be mildly superluminal in curved spacetimes. Related to this, small scattering time advances relative to the curved background can emerge from known effective field theory coefficients for photons or gravitons. We clarify why these results are not in contradiction with causality, analyticity or Lorentz invariance, and highlight various subtleties that arise when dealing with superluminalities and time advances in the gravitational context. Consistent low-energy effective theories are shown to self-protect by ensuring that any time advance and superluminality calculated within the regime of validity of the effective theory is necessarily unresolvable, and cannot be argued to lead to a macroscopically larger lightcone. Such considerations are particularly relevant for putting constraints on cosmological and gravitational effective field theories and we provide explicit criteria to be satisfied so as to ensure causality.