  Alternative theories of gravity predict modifications in the propagation of
gravitational waves (GW) through space-time. One of the smoking-gun predictions
of such theories is the change in the GW luminosity distance to GW sources as a
function of redshift relative to the electromagnetic (EM) luminosity distance
expected from EM probes. We propose a multi-messenger test of the theory of
general relativity from the propagation of gravitational waves by combining EM
and GW observations to resolve these issues from GW sources without EM
counterparts (which are also referred to as dark standard sirens). By using the
relation between the geometric distances accessible from baryon acoustic
oscillation measurements, and luminosity distance measurements from the GW
sources, we can measure any deviation from the general theory of relativity via
the GW sources of unknown redshift that will be detectable by networks of GW
detectors such as LIGO, Virgo, and KAGRA. Using this technique, the fiducial
value of the frictional term can be measured to a precision
$\Xi_0=0.98^{+0.04}_{-0.23}$ after marginalizing over redshift dependence,
cosmological parameters, and GW bias parameters with $\sim 3500$ dark standard
sirens of masses $30\,\rm M_\odot$ each distributed up to redshift $z=0.5$. For
a fixed redshift dependence, a value of $\Xi_0=0.99^{+0.02}_{-0.02}$ can be
measured with a similar number of dark sirens. Application of our methodology
to the far more numerous dark standard sirens detectable with next generation
GW detectors, such as LISA, Einstein Telescope and Cosmic Explorer, will allow
achievement of higher accuracy than possible from use of bright standard
sirens.
