On the influence of the cosmological constant on gravitational lensing in small systems

TL;DR

This paper investigates how the cosmological constant influences gravitational lensing in small systems, showing minor effects on image magnification, Einstein ring size, and time delay, especially negligible for near lenses.

Contribution

It provides a detailed calculation of Lambda's effects on lensing observables in the weak deflection limit within the Schwarzschild-de Sitter metric, updating previous results.

Findings

Lambda causes slight demagnification of unresolved images

The Einstein ring radius decreases due to Lambda

Time delay between images increases with Lambda

Abstract

The cosmological constant Lambda affects gravitational lensing phenomena. The contribution of Lambda to the observable angular positions of multiple images and to their amplification and time delay is here computed through a study in the weak deflection limit of the equations of motion in the Schwarzschild-de Sitter metric. Due to Lambda the unresolved images are slightly demagnified, the radius of the Einstein ring decreases and the time delay increases. The effect is however negligible for near lenses. In the case of null cosmological constant, we provide some updated results on lensing by a Schwarzschild black hole.