Rigorous Approach to the Gravitational Lensing

TL;DR

This paper rigorously analyzes weak gravitational lensing by solving null geodesic equations in various cosmological backgrounds, confirming the correctness of conventional lensing results even with a cosmological constant.

Contribution

It provides a detailed, accurate setup for gravitational lensing analysis and confirms that standard methods are valid in a universe with a cosmological constant and in general FRW backgrounds.

Findings

Conventional lensing results hold in a universe with mbda.

The analysis confirms no correction is needed for mbda in lensing.

Methodology applies to generic FRW cosmologies.

Abstract

We revisit a weak gravitational lensing problem by constructing a setup which describes the actual system as accurately as possible and solving the null geodesic equations. Details are given for the case of a Universe driven only by a cosmological constant, \Lambda, which confirm the conventional results: The conventional lensing analysis is correct as it is, without any need for correction of O(\Lambda). We also treat the cases of the lensing in generic FRW backgrounds.