Effect of Peculiar Motion in Weak Lensing
arXiv:0810.0180 · doi:10.1103/PhysRevD.78.123530
Abstract
We study the effect of peculiar motion in weak gravitational lensing. We derive a fully relativistic formula for the cosmic shear and the convergence in a perturbed Friedmann Universe. We find a new contribution related to galaxies peculiar velocity. This contribution does not affect cosmic shear in a measurable way, since it is of second order in the velocity. However, its effect on the convergence (and consequently on the magnification, which is a measurable quantity) is important, especially for redshifts z < 1. As a consequence, peculiar motion modifies also the relation between the shear and the convergence.
11 pages, 7 figures; v2: discussion on the reduced shear added (5.C), additional references, version accepted in PRD; v3: mistakes corrected in eqs. (26), (31), (33) and (44); results unchanged
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