The direct detection of gravitational waves from binary mergers has been hailed as the discovery of the century. In the light of recent evidence on the existence of gravitational waves, it is now possible to know about the properties of matter under extreme conditions in compact astrophysical objects and different dynamical spacetimes. The foremost theme of the present article is to bring out the various features of the interaction between photons and gravitons that can be used in astrophysical observations. The effective action of interacting photons containing light–matter coupling and self-interaction term is constructed by eliminating the graviton degrees of freedom coupled to both matter and photons. It is shown that the equation of state of matter can be probed from the dynamics of light in this theory. The vacuum birefringence is also shown to be a generic property in this theory that arises from the nonlinear nature of the self-interaction between gauge fields. Further, the non-local nature of quantum effective action with modified dispersion relation is also discussed in great detail. The above results also open an alternate way to infer the properties of gravitational waves without their direct measurement using the features of photon–graviton interaction. © 2021, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.