MG11 
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Lensing Effects on Gravitational Waves in a Clumpy Universe

The distance-redshift relation via gravitational waves in the clumpy universe is simulated numerically by taking account of 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 the 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 former, the distance-redshift relation for the fully homogeneous and isotropic universe is reproduced with small distance dispersion, whereas, in the latter, the distance dispersion is larger. We may obtain the information about the typical mass of lens objects through the distance-redshift relation gleaned through observation of gravitational waves of various wavelengths.