Quantium field theory of mutually inteeracting particles in expanding universes

The authors discuss the quantum field theory of mutually interacting particles in a classical curved space-time (external gravitational field) using the S-matrix approach in the interaction picture. Because the external field is capable of producing pairs out of the vacuum, the specification of the outcome of the pure mutual interaction is based on the registration of the participating particles which show no vacuum creation. A detailed analysis of the corresponding added-up probability is given. For free fields, a gravitational amplification (for boson) or attenuation (for fermions) of the ingoing particle content can be read off from the mean value of the particle number operator. The general results are illustrated and further complemented by the discussion of 3 examples