The role of Lambda in the cosmological lens equation

TL;DR

This paper investigates how the cosmological constant Lambda influences gravitational lensing in the Schwarzschild-de Sitter spacetime, revealing two novel effects on bending angles and redshifts that are very small but theoretically significant.

Contribution

It introduces two new effects of Lambda on gravitational lensing that cannot be explained by traditional angular diameter distance calculations.

Findings

Lambda adds a 2m b Lambda/3 term to the bending angle.

Lambda causes a difference in redshifts of multiple images.

Effects are very small for typical astrophysical systems.

Abstract

The cosmological constant Lambda affects cosmological gravitational lensing. Effects due to Lambda can be studied in the framework of the Schwarzschild-de Sitter spacetime. Two novel contributions, which can not be accounted for by a proper use of angular diameter distances, are derived. First, a term 2m b Lambda/3 has to be added to the bending angle, where "m" is the lens mass and "b" the impact parameter. Second, Lambda brings about a difference in the redshifts of multiple images. Both effects are quite small for real astrophysical systems (contribution to the bending < 0.1 microarcsec and difference in redshift < 10^{-7}).