lensing on an expanding metric

Why is it possible to treat gravitational lensing on an expanding background metric as if it was Minkowskian, weakly perturbed by the gravitational potential? If this is related to a property of photons, to which other particle trajectories would this apply?

bonus question: What’s \(\sqrt[\mathrm{i}]{\mathrm{i}}\) with \(\mathrm{i} = \sqrt{-1}\)?