The Speed of Gravity

TL;DR

This paper investigates how quantum effects in effective field theory cause the speed of gravitational waves to deviate slightly from the speed of light, with implications for Lorentz invariance and cosmological observations.

Contribution

It demonstrates that quantum loop effects and higher spin interactions can lead to superluminal gravitational wave speeds in certain backgrounds, challenging assumptions of luminal propagation.

Findings

Gravitational wave speed can be superluminal at low energies on NEC-preserving backgrounds.

Loop corrections from Standard Model fields affect the gravitational wave speed.

The speed of gravitational waves approaches luminal at high energies due to Lorentz invariance.

Abstract

Within the standard effective field theory of General Relativity, we show that the speed of gravitational waves deviates, ever so slightly, from luminality on cosmological and other spontaneously Lorentz-breaking backgrounds. This effect results from loop contributions from massive fields of any spin, including Standard Model fields, or from tree level effects from massive higher spins $s \ge 2$. We show that for the choice of interaction signs implied by S-matrix and spectral density positivity bounds suggested by analyticity and causality, the speed of gravitational waves is in general superluminal at low-energies on NEC preserving backgrounds, meaning gravitational waves travel faster than allowed by the metric to which photons and Standard Model fields are minimally coupled. We show that departure of the speed from unity increases in the IR and argue that the speed inevitably returns to luminal at high energies as required by Lorentz invariance. Performing a special tuning of the EFT so that renormalization sensitive curvature-squared terms are set to zero, we find that finite loop corrections from Standard Model fields still lead to an epoch dependent modification of the speed of gravitational waves which is determined by the precise field content of the lightest particles with masses larger than the Hubble parameter today. Depending on interpretation, such considerations could potentially have far-reaching implications on light scalar models, such as axionic or fuzzy cold dark matter.