  We analyse the speed of gravitational waves in coupled Galileon models with
an equation of state $\omega_\phi=-1$ now and a ghost-free Minkowski limit. We
find that the gravitational waves propagate much faster than the speed of light
unless these models are small perturbations of cubic Galileons and the Galileon
energy density is sub-dominant to a dominant cosmological constant. In this
case, the binary pulsar bounds on the speed of gravitational waves can be
satisfied and the equation of state can be close to -1 when the coupling to
matter and the coefficient of the cubic term of the Galileon Lagrangian are
related. This severely restricts the allowed cosmological behaviour of Galileon
models and we are forced to conclude that Galileons with a stable Minkowski
limit cannot account for the observed acceleration of the expansion of the
universe on their own. Moreover any sub-dominant Galileon component of our
universe must be dominated by the cubic term. For such models with gravitons
propagating faster than the speed of light, the gravitons become potentially
unstable and could decay into photon pairs. They could also emit photons by
Cerenkov radiation. We show that the decay rate of such speedy gravitons into
photons and the Cerenkov radiation are in fact negligible. Moreover the time
delay between the gravitational signal and light emitted by explosive
astrophysical events could serve as a confirmation that a modification of
gravity acts on the largest scales of the Universe.
