EXPONENTIAL-GROWTH OF DISTANCE BETWEEN NEARBY RAYS DUE TO MULTIPLE GRAVITATIONAL SCATTERINGS

We give an estimate of the relative error in the angular measurement o f observations for high-redshift objects induced by gravitational scat terings (lensing). Gunn concluded in 1967 that the gravitational scatt erings by galaxies induce a relative error of a few percent in observa tions for objects at z = 1. This estimate has been considered as a fun damental limitation of accuracy of the angular measurements in observa tional cosmology. In multiple gravitational scatterings, the bending a ngle of a single ray grows through the random work process. Gunn assum ed that the difference of nearby rays also grows through the random wa lk process. However, the distance between nearby photons grows exponen tially because the two rays suffer coherent scatterings by the same sc attering object. This exponential growth continues as long as the scat tering is coherent. In the case of scattering by individual galaxies, the exponential growth continues until the angular distance reaches 1' or so. The relative error of the angular measurements under 1' due to the exponential growth is similar to 30% at z = 1 and exceeds 100% at z = 3, when the density parameter of galaxies is 0.2. The effects of clusters of galaxies or superclusters are more difficult to estimate a ccurately but might be significant. In the case of superclusters, the angular measurements up to a few degrees could be affected.