Deflection of light and time delay in closed Einstein-Straus solution

TL;DR

This paper studies how light deflection and time delay are affected by a spherically symmetric mass in a closed universe with a positive cosmological constant, using a new integration method and applying it to a specific quasar lensing case.

Contribution

It introduces a differential equation integration method to compute light deflection and delay in the Einstein-Straus model with positive cosmological constant for a closed universe.

Findings

Light deflection and time delay depend on the scale factor value.

A positive cosmological constant reduces light bending.

Results align with previous findings for flat universe when scale factor is large.

Abstract

We investigate strong lensing by a spherically symmetric mass distribution in the framework of the Einstein-Straus solution with positive cosmological constant and concentrate on the case of a spatially closed Universe ($k=+1$). We develop a method based on integration of differential equations in order to make possible the computation of light deflection and time delay. By applying our results to the lensed quasar SDSS J1004+4112, we find that the bending of light and time delay depend on wether the present value of the scale factor $a_0$ is or is not much smaller than a value close to $9.1 \cdot 10^{26} \mbox{m}$. Beyond this value, the results are almost the same as for the spatially flat Universe. Moreover, it turns out that a positive cosmological constant attenuates the light bending in agreament with Rindler and Ishak's finding.