Effect of Accelerated Global Expansion on Bending of Light

TL;DR

This paper investigates how the changing rate of cosmic expansion influences light bending around black holes in an evolving universe, extending previous models to more general cosmological backgrounds.

Contribution

It introduces a numerical analysis of light deflection in a McVittie spacetime with varying Hubble parameter, generalizing prior work on cosmological effects on gravitational lensing.

Findings

Bending angle depends on the rate of change of H(t)

Different observer frames measure varying deflection angles

Expansion rate variation influences gravitational lensing predictions

Abstract

In 2007 Rindler and Ishak showed that, contrary to previous claims, the value of the cosmological constant does have an effect on light deflection by a gravitating object in an expanding universe, modeled by a Schwarzschild-de~Sitter spacetime. In this paper we consider light bending in the more general situation of a gravitating object in a cosmological background with varying expansion rate $H(t)$. We calculate numerically the null geodesics representing light rays deflected by a black hole in an accelerating Friedmann-Lema\^itre-Robertson-Walker universe, modeled by a McVittie metric. Keeping the values of the distances from the observer to the lensing object and to the source fixed, we plot the dependence of the bending angle measured by two different sets of observers in this spacetime on the rate of change of $H(t)$.