Large-scale structure effects on the gravitational lens image positions and time delay

We compute the fluctuations in gravitational lens image positions and time delay caused by large-scale structure correlations. We show that these fluctuations can be expressed as a simple integral over the density power spectrum. Using the COBE normalization we find that positions of objects at cosmological distances are expected to deviate from their true positions by few arcminutes. These deflections are not directly observable. The positions of the images relative to one another fluctuate by a few percent of the relative separation, implying that one does not expect multiple images to be produced by large-scale structures. Nevertheless, the fluctuations are larger than the observational errors on the positions and affect reconstructions of the lens potential. The time delay fluctuations have a geometrical and a gravitational contribution. Both are much larger than the expected time delay from the primary lens, but partially cancel each other. We find that large-scale structure weakly affects the time delay and time delay measurements can be used as a probe of the distance scale in the universe.