  We identify a scalar-tensor model embedded in the Horndeski action whose
cosmological background and linear scalar fluctuations are degenerate with the
concordance cosmology. The model admits a self-accelerated background expansion
at late times that is stable against perturbations with a sound speed
attributed to the new field that is equal to the speed of light. While
degenerate in scalar fluctuations, self-acceleration of the model implies a
present cosmological tensor mode propagation at < 95% of the speed of light
with a damping of the wave amplitude that is > 5% less efficient than in
general relativity. We show that these discrepancies are endemic to
self-accelerated Horndeski theories with degenerate large-scale structure and
are tested with measurements of gravitational waves emitted by events at
cosmological distances. Hence, gravitational-wave cosmology breaks the dark
degeneracy in observations of the large-scale structure between two
fundamentally different explanations of cosmic acceleration - a cosmological
constant and a scalar-tensor modification of gravity. The gravitational wave
event GW150914 recently detected with the aLIGO instruments and its potential
association with a weak short gamma-ray burst observed with the Fermi GBM
experiment may have provided this crucial measurement.
