  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.
