THE EFFECT OF GRAVITATIONAL SCATTERING ON THE ANISOTROPY OF THE COSMIC BACKGROUND-RADIATION

The homogeneity of the cosmic microwave background radiation (CBR) is one of the most severe constraints for theories of structure formation in the universe. We investigated the effect of the gravitational scattering (lensing) of galaxies, clusters of galaxies, and superclusters on the anisotropy of the CBR by numerical simulations. Although this effect was thought to be unimportant, we found that the gravitational scatterings by superclusters can significantly reduce the anisotropy of the CBR. We took into account the exponential growth of the distance between two rays due to multiple scatterings. The bending angle of each ray grows through a random walk process. On the other hand, the difference between two rays grows exponentially while it is small. This exponential growth is caused by coherent scatterings that the two rays suffer and was neglected in the previous studies. The gravitational scattering by superclusters reduces the observed temperature anisotropy of the CBR at the present time by similar to 40%-60% from that at the recombination time for an angular scale up to a few degrees if the supercluster were formed at z = 2-4.