  The clustering of gravitational waves in luminosity distance space is
emerging as a promising probe of the growth of structure. Just like for
galaxies, its osbervation is subject to a number of relativistic corrections
that affect the measured signal and need to be accounted for when fitting
theoretical models to the data. We derive the full expression for the number
count of gravitational waves in luminosity distance space, including all
relativistic corrections, in LCDM and in scalar-tensor theories with luminal
propagation of tensors. We investigate the importance of each relativistic
effect and the detectability of the total signal by current and planned GW
detectors. We consider also supernovae in luminosity distance space,
highlighting the differences with gravitational waves in the case of
scalar-tensor theories. We carry out a thorough comparison among the number
count of gravitational waves and supernovae in luminosity distance space, and
that of galaxies in redshift space. We show how the relativistic corrections
contain useful complementary information on the growth of perturbations and on
the underlying theory of gravity, highlighting the synergy with other
cosmological probes.

Cosmology and Nongalactic Astrophysics