Improved concepts for the discussion of mutually interacting quantum fields in Robertson-Walker universes

We discuss quantum field theory of mutually interacting particles in given unquantized Robertson-Walker universes using an S-matrix approach. To improve this approach, we introduce the concepts of ‘‘pair-including transition probability’’ and ‘‘specified mean number.’’ Both are based on the specification of not only the in state but also the out state. Beyond that it is taken into account that every process is accompanied by gravitational pair production out of the space-time background. The corresponding expressions can be expressed by in-in amplitudes, so that Feynman diagram rules can be established. To demonstrate the advantage of the new concepts, we discuss for conformally coupled Klein-Gordon fields the Compton effect in the ${\phi }^2$ ${\psi }^2$ model and demonstrate the effect of induced gravitational amplification in a direct and very transparent way.