Gravitational lens on de-Sitter background

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.

arXiv comment12 pages, 8 figures, typos corrected, 2 references added, accepted for PRD

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Cited by in corpus (6)

• Time Delay of Light in the Gravitational lensing of Supermassive Black Holes in Dark Matter Halos
• Gravitational Lensing of Spherically Symmetric Black Holes in Dark Matter Halos
• Gravitational lens on a static optical constant-curvature background: Its application to Weyl gravity model
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• Probing dark fluids and modified gravity with gravitational lensing
• The influence of cosmological constant on light deflection in rotating spacetimes via the generalized Gibbons-Werner method