  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
