Effect of multiple gravitational lensing on the anisotropy of the cosmic background radiation

We investigated smoothing of the cosmic background radiation (CBR) by multiple gravitational lensing. The CBR is gravitationally scattered by galaxies, clusters of galaxies, and superclusters during the travel from the last scattering surface. Although the effect ofthe gravitational lensing was thought to be unimportant, we found that the multiple gravitational lensing by clusters of galaxies or by superclusters can reduced by a large factor. This result is explained by the fact that the distance between two light rays grows exponentially though multiple gravitational lensing. If such structures were formed at z = 2 - 5 and contain a large fraction of the mass of the universe (Omega(s) > 0.5), then multiple gravitational lensing can reduce the temperature anisotropy of the CBR by 40-60%, approximately up to a degree scale.