Light Deflection, Lensing, and Time Delays from Gravitational Potentials and Fermat's Principle in the Presence of a Cosmological Constant

Abstract

The contribution of the cosmological constant to the deflection angle and the time delays are derived from the integration of the gravitational potential as well as from Fermat's Principle. The findings are in agreement with recent results using exact solutions to Einstein's equations and reproduce precisely the new $\Lambda$-term in the bending angle and the lens equation. The consequences on time delay expressions are explored. While it is known that $\Lambda$ contributes to the gravitational time delay, it is shown here that a new $\Lambda$-term appears in the geometrical time delay as well. Although these newly derived terms are perhaps small for current observations, they do not cancel out as previously claimed. Moreover, as shown before, at galaxy cluster scale, the $\Lambda$ contribution can be larger than the second-order term in the Einstein deflection angle for several cluster lens systems.

6 pages, 1 figure, matches version published in PRD

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• The Relevance of the Cosmological Constant for Lensing
• Mass function and particle creation in Schwarzschild-de Sitter spacetime
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• Geometrization of light bending and its application to SdSw spacetime
• On lensing by a cosmological constant
• More on Lensing by a Cosmological Constant
• Direct Probe of Dark Energy through Gravitational Lensing Effect
• Beyond lensing by the cosmological constant
• Gravitational Lensing Corrections in Flat LambdaCDM Cosmology
• Lambda does not Lens: Deflection of Light in the Schwarzschild-de Sitter Spacetime
• Generalized Swiss-cheese cosmologies: Mass scales
• Generalized Gibbons-Werner method for stationary spacetimes
• Time Delay in Swiss Cheese Gravitational Lensing
• On the effect of the cosmological expansion on the gravitational lensing by a point mass
• Exploring light deflection and black hole shadows in Rastall theory with plasma effects
• Cosmic Time Slip: Testing Gravity on Supergalactic Scales with Strong-Lensing Time Delays
• Cosmological applications of the Brown-York quasilocal mass
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• Effect of the spatial curvature on light bending and time delay in curved Einstein-Straus--de Sitter spacetime
• Electrodynamics in curved spacetime: Gravitationally-induced constitutive equations and the spacetime index of refraction