Emergent gravitational dynamics from a photon action with an effective refractive index

Abstract

I investigate a gravitational framework derived from a variational principle applied to the action of a photon observed from a non-inertial reference frame. We define an effective refractive index associated with the gravitational field. The resulting photon trajectories correspond to geodesic of an effective  optical metric. In the weak-field limit the theory predicts a modified gravitational potential that can explain the flat galactic rotation curves without dark matter. At cosmological scales the model generates an effective gravitational energy density that lead to acelerated cosmic expansion without introducing a cosmological constant. Possible observational consequences are discussed