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We investigate infrared divergences of expectation values of products of field operators in a class of curved space-times. The massless minimally coupled scalar field and the linearized gravitational field, quantized on a subset of spatially flat Robertson-Walker background metrics, have such divergences for an apparently natural choice of state vectors. For those states which give a large infrared contribution to the energymomentum tensor, we show that these metrics cannot be self-consistent solutions of Einstein's equations. Finally, we show that such divergences cannot evolve dynamically in these models from initial conditions which are free of them. These divergences provide one possible criterion for limiting the acceptable choices of state vectors in curved space-time.
Ford et al. (1977) studied this question.