Lensing in the McVittie metric

TL;DR

This paper examines how cosmological expansion influences gravitational lensing by a point mass using the McVittie metric, finding that at leading order, expansion does not affect the bending angle.

Contribution

It provides an analytic expression for light bending in the McVittie metric with constant Hubble parameter, showing expansion effects are negligible at leading order.

Findings

Bending angle unaffected by cosmological expansion at leading order

Analytic expression derived for lensing in McVittie metric with constant Hubble

Expansion effects are minimal in the leading order approximation

Abstract

We investigate the effect of the cosmological expansion on the bending of light due to an isolated point-like mass. We adopt McVittie metric as the model for the geometry of the lens. Assuming a constant Hubble factor we find an analytic expression involving the bending angle, which turns out to be unaffected by the cosmological expansion at the leading order.