Effect of accelerated global expansion on the bending of light

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. In their work they considered a Schwarzschild–de Sitter (SdS) spacetime, which has a constant asymptotic expansion rate \(H_0\). A model with a time-dependent H(t) was studied by Kantowski et al., who consider in their 2010 paper a “Swiss-cheese” model of a Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime with an embedded SdS bubble. In this paper, we generalize the Rindler and Ishak model to time-varying H(t) in another way, by considering light bending in a McVittie metric representing a gravitating object in a FLRW cosmological background. We carry out numerical simulations of the propagation of null geodesics in different McVittie spacetimes, in which we keep the values of the distances from the observer to the lensing object and to the source fixed, and vary the form of H(t).