Decay of massive particles in Robertson-Walker universes with statically bounded expansion laws

Abstract

The authors study mutually interacting quantum fields in 3-flat Robertson-Walker universes. Using the interaction picture and an in-out approach based on an S matrix, they give an exact calculation of the decay of a massive scalar Phi particle into two massless scalar Psi particles (both conformally coupled to the background) in lowest order of the ( lambda /a( eta )) Phi Psi 2 interaction. The cosmic scale factor a( eta ) is thereby specified (i) as the step-expansion law, and (ii) as the tanh-expansion law which represents the prototype of a smoothed-out step law. These a( eta ) are typical representatives of monotonic expansions with asymptotically static in and out regions. The characteristic modifications of the Minkowskian decay spectrum like the double-resonance structure are discussed. Comparison of amplitudes and decay probabilities for (i) and (ii) demonstrates that smoothing-out the step introduces a gravitational influence of non-vanishing duration, which leads essentially to finite corrections of the step results. Additionally, it can be shown that the massive particles which are gravitationally created out of the background, decay as well and contribute to the number of outgoing massless particles. From the results obtained, the general structure of amplitudes, probabilities, and decay rates holding for all statically bounded monotonic expansion laws can be read off.