Causality in Curved Spacetimes: The Speed of Light & Gravity

TL;DR

This paper examines how low-energy effective field theories of QED and gravity can exhibit superluminal speeds in curved spacetimes without violating causality, emphasizing the importance of theoretical consistency and effective theory validity.

Contribution

It clarifies why superluminalities in curved spacetime effective theories do not contradict causality and provides criteria to ensure these theories remain consistent.

Findings

Superluminal speeds are consistent with causality in effective theories.

Time advances are unresolvable within the effective theory regime.

Criteria are provided to ensure causality in cosmological and gravitational theories.

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.