Gravitational Lensing by a structure in a cosmological background

TL;DR

This paper compares exact general relativistic calculations of gravitational lensing by a cosmological structure with the thin lens approximation, finding good agreement for certain density profiles and negligible observational differences.

Contribution

It demonstrates the validity of the thin lens approximation in a cosmological setting using an exact relativistic model with various density profiles.

Findings

Thin lens approximation matches exact calculations for modified NFW profiles with voids.

Normal NFW profile shows deviations from exact relativistic results.

No significant observational differences in strong and weak lensing data.

Abstract

We use an exact general relativistic model structure within an FRW cosmological background based on a LTB metric to study the gravitational lensing by a cosmological and dynamical structure. Using different density profiles for the model structure, the deviation angle and the time delay through the gravitational lensing has been studied by solving the geodesic equations. The results of these exact calculations have been compared to the thin lens approximation. We have shown that the result for the thin lens approximation based on a modified NFW density profile with a void before going over to the FRW background matches very well with the exact general relativistic calculations. However, the thin lens approximation based on a normal NFW profile does differ from the exact relativistic calculation. The difference is more the less compact the structure is. We have also looked at the impact of our calculation on the observational interpretation of arcs in the case of strong lensing and also the reduced shear in the case of weak lensing. No significant difference has been seen in the data available.