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We consider a relativistic Ansatz for the vacuum expectation values (VEVs) ofa quantum field on a globally hyperbolic space-time which is motivated bycertain Euclidean field theories. The Yang-Feldman asymptotic condition w.r.t.a "in"-field in a quasi-free representation of the canonic commutationrelations (CCR) leads to a solution of this Ansatz for the VEVs. A GNS-likeconstruction on a non-degenerate inner product space then gives local,covariant quantum fields with indefinite metric on a globally hyperbolicspace-time. The non-trivial scattering behavior of quantum fields is analyzedby construction of the "out"-fields and calculation of the scattering matrix. Anew combined effect of non-trivial quantum scattering and non-stationarygravitational forces is described for this model, as quasi-free "in"- fieldsare scattered to "out"-fields which form a non quasi-free representations ofthe CCR. The asymptotic condition, on which the construction is based, isverified for the concrete example of de Sitter space-time

An Indefinite Metric Model for Interacting Quantum Fields on Globally Hyperbolic Space-Times