Effect of Peculiar Motion in Weak Lensing

TL;DR

This paper derives a relativistic formula for weak lensing effects, highlighting how peculiar velocities influence convergence and magnification, especially at redshifts below 1, and alters shear-convergence relations.

Contribution

It introduces a new relativistic correction accounting for galaxy peculiar velocities in weak lensing analysis, impacting convergence and magnification measurements.

Findings

Peculiar velocities significantly affect convergence at z<1.

The new velocity-related term does not measurably impact cosmic shear.

Peculiar motion modifies the shear-convergence relationship.

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.