Gravitational lens on de-Sitter background

TL;DR

This paper investigates gravitational lensing in de-Sitter and anti-de Sitter backgrounds, highlighting differences in lens equations and image separation influenced by the cosmological constant and background geometry.

Contribution

It introduces a framework for analyzing gravitational lensing in dS/AdS backgrounds, incorporating horizon effects and hyperbolic/trigonometric geometries, extending beyond flat spacetime models.

Findings

Angular separation decreases in dS and increases in AdS at third order.

Deflection angle of light is independent of the cosmological constant term.

Separation angle of images varies with the cosmological constant and background geometry.

Abstract

Gravitational lenses are examined in de-Sitter (dS) background, for which the existence of the dS horizon is taken into account and hyperbolic trigonometry is used together with the hyperbolic angular diameter distance. Spherical trigonometry is used to discuss a gravitational lens in anti-de Sitter (AdS) background. The difference in the form among the dS/AdS lens equations and the exact lens equation in Minkowski background begins at the third order, when a small angle approximation is used in terms of lens and source planes. The angular separation of lensed images is decreased by the third-order deviation in the dS lens equation, while it is increased in AdS. In the present framework on the dS/AdS backgrounds, we discuss also the deflection angle of light, which does not include any term of purely the cosmological constant. Despite the different geometry, the deflection angle of light rays in hyperbolic and spherical geometry can take the same form. Through a coupling of the cosmological constant with lens mass, the separation angle of multiple images is larger (smaller) in dS (AdS) than in the flat case, for a given mass, source direction, and angular diameter distances among the lens, receiver and source.