  The detection of gravitational waves (GWs) and an accompanying
electromagnetic (E/M) counterpart have been suggested as a future probe for
cosmology and theories of gravity. In this paper, we present calculations of
the luminosity distance of sources taking into account inhomogeneities in the
matter distribution that are predicted in numerical simulations of structure
formation. In addition, we show that inhomogeneities resulting from clustering
of matter can mimic certain classes of modified gravity theories, or other
effects that dampen GW amplitudes, and deviations larger than $\delta \nu \sim
\mathcal{O}(0.1)\ (99\%\ \rm{C.L.})$ to the extra friction term $\nu$, from
zero, would be necessary to distinguish them. For these, we assume mock GWs
sources, with known redshift, based on binary population synthesis models,
between redshifts $z=0$ and $z=5$. We show that future GW detectors, like
Einstein Telescope or Cosmic Explorer, will be needed for strong constraints on
the inhomogeneity parameters and breaking the degeneracy between modified
gravity effects and matter anisotropies by measuring $\nu$ at $5 \%$ and $1 \%$
level with $100$ and $350$ events respectively.
