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

Understand

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.