  The distance-redshift relation determined by means of gravitational waves in
the clumpy universe is simulated numerically by taking into account the effects
of gravitational lensing. It is assumed that all of the matter in the universe
takes the form of randomly distributed point masses, each of which has the
identical mass $M_L$. Calculations are carried out in two extreme cases:
$\lambda\gg GM_L/c^2$ and $\lambda\ll GM_L/c^2$, where $\lambda$ denotes the
wavelength of gravitational waves. In the first case, the distance-redshift
relation for the fully homogeneous and isotropic universe is reproduced with a
small distance dispersion, whereas in the second case, the distance dispersion
is larger. This result suggests that we might obtain information about the
typical mass of lens objects through the distance-redshift relation gleaned
through observation of gravitational waves of various wavelengths. In this
paper, we show how to set limitations on the mass $M_L$ through the observation
of gravitational waves in the clumpy universe model described above.

Astrophysics