Time Delay in Swiss Cheese Gravitational Lensing

TL;DR

This paper calculates gravitational lensing time delays in a Swiss cheese universe model, revealing small but significant deviations from conventional theory due to the cosmological constant and mass distribution effects.

Contribution

It introduces a novel approach to computing lensing delays considering the cosmological constant and embedded mass, highlighting limitations of traditional linear lensing models.

Findings

Cosmological constant effects on time delays are minimal (~0.002%) for large lenses.

Differences from conventional models can reach ~4% for large lenses.

Traditional lensing theory neglects the lens mass contribution to the universe's mean density.

Abstract

We compute time delays for gravitational lensing in a flat LambdaCDM Swiss cheese universe. We assume a primary and secondary pair of light rays are deflected by a single point mass condensation described by a Kottler metric (Schwarzschild with Lambda) embedded in an otherwise homogeneous cosmology. We find that the cosmological constant's effect on the difference in arrival times is non-linear and at most around 0.002% for a large cluster lens; however, we find differences from time delays predicted by conventional linear lensing theory that can reach ~4% for these large lenses. The differences in predicted delay times are due to the failure of conventional lensing to incorporate the lensing mass into the mean mass density of the universe.