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Quantum field theory in curved space-times is a well developed area in mathematical physics which has had important phenomenological applications to the very early universe. However, it is not commonly appreciated that on time-dependent space-times---including the simplest cosmological models---dynamics of quantum fields is not unitary in the standard sense. This issue is first explained with an explicit example, and it is then shown that a generalized notion of unitarity does hold. The generalized notion allows one to correctly pass to the Schr\"odinger picture starting from the Heisenberg picture used in the textbook treatments. Finally, we indicate how these considerations can be extended from simple cosmological models to general globally hyperbolic space-times.
Agulló et al. (Tue,) studied this question.
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