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.
Highlights
In this new era of gravitational wave astronomy, it is especially important to understand how gravitational waves propagate
effective field theory (EFT) coefficients, the light cone inferred from the low energy sound speed of matter always lies inside the light cone of gravitational waves and is never exactly at the same speed
In particular we show that the low energy speed of the gravitational wave depends on the field content of the high-energy completion, and on the spin of the lightest massive particle that is integrated out to derive the low energy Wilsonian action
Summary
In this new era of gravitational wave astronomy, it is especially important to understand how gravitational waves propagate. (v) Our results remain valid when considering purely quartic curvature corrections, such as those known to arise in the low energy string theory effective action, for which gravitational waves travel superluminally on NEC preserving backgrounds. EFT coefficients (either as inferred from explicit integration of fields or from positivity bounds or as implied from string theory), the light cone inferred from the low energy sound speed of (minimally coupled) matter always lies inside the light cone of gravitational waves and is never exactly at the same speed. We explore the leading curvature-squared contributions to the low energy EFT for gravity in Sec. III and identify their effect on the speed of gravitational waves on FLRW and on static warped backgrounds. As is standard, slightly abuse the EFT operator counting terminology and refer to Riemannn operators as dimension-2n operators evvaerinouthsoduigmhetnhseiyoninscPludkehaknð∂in2hfiÞnni=teMnkPuþlm3nb−e4r of operators þ Á Á Á
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