`Superluminal' Photon Propagation in QED in Curved Spacetime is Dispersive and Causal

It is now well-known that vacuum polarisation in QED can lead to super- luminal low-frequency phase velocities for photons propagating in curved spacetimes. In a series of papers, we have shown that this quantum phenomenon is dispersive and have calculated the full frequency dependence of the refractive index, explaining in detail how causality is preserved and various familiar results from quantum field theory such as the Kramers-Kronig dispersion relation and the optical theorem are realised in curved spacetime. These results have been criticised in a recent paper by Akhoury and Dolgov [1], who assert that photon propagation is neither dispersive nor necessarily causal. In this note, we point out a series of errors in their work which have led to this false conclusion