On lensing by a cosmological constant

TL;DR

This paper clarifies that the cosmological constant Lambda does not directly affect gravitational light bending, and apparent Lambda-dependent effects are frame-dependent and not true lensing phenomena.

Contribution

It derives an expression showing no explicit Lambda dependence in cosmological light bending, clarifying misconceptions about Lambda's role in gravitational lensing.

Findings

Lambda does not explicitly influence light deflection in cosmology.

Apparent Lambda effects are due to observer motion and cosmic acceleration, not actual lensing.

Standard lensing results remain valid without modifications for Lambda.

Abstract

Several recent papers have suggested that the cosmological constant Lambda directly influences the gravitational deflection of light. We place this problem in a cosmological context, deriving an expression for the linear potentials which control the cosmological bending of light, finding that it has no explicit dependence on the cosmological constant. To explore the physical origins of the apparent Lambda-dependent potential that appears in the static Kottler metric, we highlight the two classical effects which lead to the aberration of light. The first relates to the observer's motion relative to the source, and encapsulates the familiar concept of angular-diameter distance. The second term, which has proved to be the source of debate, arises from cosmic acceleration, but is rarely considered since it vanishes for photons with radial motion. This apparent form of light-bending gives the appearance of curved geodesics even within a flat and homogeneous universe. However this cannot be construed as a real lensing effect, since its value depends on the observer's frame of reference. Our conclusion is thus that standard results for gravitational lensing in a universe containing Lambda do not require modification, with any influence of Lambda being restricted to negligible high-order terms.