Gravitationally induced photon entanglement in an FLRW cosmological background

In order to detect the quantum nature of gravity, the quantum-gravity-induced entanglement of masses has been proposed in both flat and curved spacetime. In this paper, we propose an analogous quantum-gravity-induced entanglement of masses protocol using photons produced in astronomical processes as the quantum systems. Unlike massive particles, the gravitational interaction between photons---intrinsically relativistic particles---simultaneously satisfies both the ``event'' and ``system'' localities. So it can provide a clear test of whether the gravitational mediator must be nonclassical based on the local operations and classical communication principle. Although the gravitationally induced entanglement between massless relativistic photons is extremely small, our quantitative calculations clarify the characteristic features of the entanglement induced by the photon's own gravitational field in astronomical process and may inspire other photon entanglement experiments.