The Correlation Function of Galaxy Ellipticities Produced by Gravitational Lensing

The gravitational potential of mass fluctuations in the universe deflects the light rays of background sources, distorting their shapes. This distortion introduces a correlation of the ellipticities of the sources lying within a given area of the sky. In this paper, we calculate the correlation of ellipticities produced by gravitational lensing, as a function of the power spectrum of density fluctuations in the universe, by generalizing an analytical method developed by Gunn. We apply this method to a model where identical objects with spherically symmetric density profiles are randomly laid down in space, and to the cold dark matter model. The possibility of detecting this correlation is discussed. An ellipticity correlation can also be caused by an intrinsic alignment of the axes of galaxies belonging to a cluster or a supercluster; however, we suggest a method by which one can distinguish between the two types of correlation. We stress the importance of reporting nondetections to the amplitude of the ellipticity correlation. This ellipticity correlation is one of the few astronomical observations that can directly probe large-scale mass fluctuations in the universe.