Investigation of the Role of the Cosmological Constant in Measurements of Strong Gravitational Lensing Systems

The cosmological constant Λ is one way of representing dark energy, which helps explain the increasing expansion of the universe.

For several decades, the contribution of Λ to the measurable bending angle of light in strong gravitational lensing systems mathematically cancelled. In 2007, an amended lens equation correctly included a Λ contribution, from which the researchers also derived an upper limit on Λ. We determine that the ideal lensing system for this constraint is essentially the largest and closest. As these are likely the ones astronomers found, adding additional, more recently discovered systems to the dataset likely will not improve the constraint present here. We compare the effect of varying the Hubble Constant by +/-2 km/s/Mpc or the matter density parameter by 0.03. These allowances caused roughly a 3-4% change, which becomes more significant with more precise calculations.

We derive a second order geometrical time delay equation to investigate the significance of Λ to such time delay measurements. We demonstrate that the first Λ term tended to be at least the same order of magnitude as the second Einstein term, and sometimes an order of magnitude larger, which is significant for precise measurements.