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In this paper, we seek to find a modified theory of gravity that accounts forthe back-reaction of QED on curved spacetime. It is already known that vacuumfluctuations induce interactions between gravity and photons. An effectiveaction for electromagnetism, which encodes the details of such quantum process,is utilized to get a set of modified Maxwell's equation and a new Lagrangianfor the dynamics of gravity. Imposition of Cauchy predictability on thesemodified Maxwell's equations lead us to a new effective metric, from which theLagrangian can be calculated. The new Lagrangian for gravity turns out to be afunction of not just the higher order derivatives of the metric tensor but alsothe polarization of the photon. This immediately results in phenomenon such asgravitational birefringence and existence of black holes with polarizationdependent event horizons.

Back-reaction of quantum processes and modified gravitational dynamics