Effect of Global Expansion on Gravitational Lensing

Traditionally it had been thought that the cosmological constant played no role in gravitational lensing, but recently it has been shown that the cosmological constant effectively changes the impact parameter and thus does have an effect on lensing. In this paper, we will examine the effects of a $\Lambda$FRW cosmology on null geodesics via numerical integration of the geodesics of the McVittie metric