A note on the effect of the cosmological constant on the bending of light

TL;DR

This paper revisits the equations governing light bending in a universe with a cosmological constant, revealing a novel way the constant influences the bending angle beyond previous models.

Contribution

It introduces a new formulation showing the cosmological constant's impact on light bending, leading to a modified expression for the bending angle.

Findings

The cosmological constant affects the impact parameter in the light bending equations.

A new expression for the bending angle is derived, differing from previous literature.

The effect appears beyond the first-order approximations in mass and cosmological constant.

Abstract

We take another look at the equations behind the description of light bending in a Universe with a cosmological constant. We show that even within the impact parameter entering into the photon's differential equation, and which is defined here with exclusive reference to the beam of light as it bends around the central mass, lies the contribution of the cosmological constant. The latter is shown to enter in a novel way into the equation. When the latter is solved our approach implies, beyond the first two orders in the mass-term and the lowest-order in the cosmological constant, a slightly different expression for the bending angle from what is previously found in the literature.