Causality in curved spacetimes: The speed of light and gravity

Abstract

Within the low-energy effective field theories of quantum electrodynamics 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 light cone. 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.

Superluminality in beyond Horndeski theory with extra scalar field

“…Let us remind that hereafter we do not use the background equations of motion when deriving the terms with derivatives and also terms involving α and β only. However, we did use background equations of motion to obtain the terms without derivatives in (20) and, in particular, to see that the term ζ • δχ vanishes. There are also terms with ζ 2 and αζ in (20) which are not written because these terms vanish in the complete quadratic action S…”

“…Now we combine DHOST Ia and k-essence components, and use the variableζ instead of ζ in S (2) χ , eq. (20). Variables α and β enter the quadratic action without time derivatives (the first term in the second line in (20), written in terms ofζ, involvesα, but this is taken care of by integration by parts ), so the variation of the total quadratic action S (2) π + S (2) χ with respect to β and α gives two constraint equations:…”

“…where Ω is defined in (20). Let us briefly discuss the stability conditions of the scalar sector in the combined system of DHOST Ia and k-essence, without assuming that the background value of Y is small.…”

Gravitational positivity bounds

“…low-energy EFT perspective [23]. Specifically, assuming that j ∼ (f /f ) ∼ (j /j ) ∼ α , we can estimate the r.h.s.…”

“…(F tree + F 1−loop ) (s, 0) with choosing Z c = 1+(16π 2 ε) −1 λ 23. Here, ε denotes an infinitesimal parameter associated with the dimensional regularization procedure: we evaluated the l.h.s.…”