Mutually Interacting Quantum Fields in an Expanding Universe: Decay of a Massive Particle

Abstract

The authors give an analysis of quantum field theory of mutually interacting fields in a 3-flat Robertson-Walker universe with regard to the questions: What are the measurable quantities? What is the related calculation scheme? The classical curved spacetime acts thereby as an external gravitational field, the influence of which is taken into account without any approximation. As a case study a mathematically rigorous calculation of the decay of a massive phi particle into two massless psi particles is given in first order of the ( lambda /a) phi psi 2 mutual interaction where a is the cosmic scale factor. The particles are conformally coupled scalar particles. The interaction picture and the in-out scheme based on an S-matrix approach are used. No renormalisation is needed. Because the external field is capable of producing pairs of massive phi particles from the vacuum, the specification of the outcome of the mutual interaction is based on the registration of massless particles in the out region. A detailed analysis of the corresponding added-up probability is given. It sheds some light on the imperfection of the usual in-out approach when applied to cosmological situations. The results are used to obtain a limit for the local applicability of flat spacetime results as cross section, decay rates etc. in a cosmological situation.