  We argue that the conventional quantum field theory in curved spacetime has a
grave drawback: The canonical commutation relations for quantum fields and
conjugate momenta do not hold. Thus the conventional theory should be denounced
and the related results revised. A Hamiltonian version of the canonical
formalism for a free scalar quantum field is advanced, and the fundamentals of
an appropriate theory are constructed. The principal characteristic feature of
the theory is quantum-gravitational nonlocality: The Schroedinger field
operator at time t depends on the metric at t in the whole 3-space.
Applications to cosmology and black holes are given, the results being in
complete agreement with those of general relativity for particles in curved
spacetime. A model of the universe is advanced, which is an extension of the
Friedmann universe; it lifts the problem of missing dark matter. A fundamental
and shocking result is the following: There is no particle creation in the case
of a free quantum field in curved spacetime; in particular, neither the
expanding universe nor black holes create particles.
