  We consider a relativistic Ansatz for the vacuum expectation values (VEVs) of
a quantum field on a globally hyperbolic space-time which is motivated by
certain Euclidean field theories. The Yang-Feldman asymptotic condition w.r.t.
a "in"-field in a quasi-free representation of the canonic commutation
relations (CCR) leads to a solution of this Ansatz for the VEVs. A GNS-like
construction on a non-degenerate inner product space then gives local,
covariant quantum fields with indefinite metric on a globally hyperbolic
space-time. The non-trivial scattering behavior of quantum fields is analyzed
by construction of the "out"-fields and calculation of the scattering matrix. A
new combined effect of non-trivial quantum scattering and non-stationary
gravitational forces is described for this model, as quasi-free "in"- fields
are scattered to "out"-fields which form a non quasi-free representations of
the CCR. The asymptotic condition, on which the construction is based, is
verified for the concrete example of de Sitter space-time.
