Cosmological particle creation as above-barrier reflection: approximation method and applications

Abstract

For the example of conformally-coupled massive Klein-Gordon particles in a Robertson-Walker universe the analogy between the Fock-space formulation of pair creation caused by the contraction and expansion of the universe on one hand and the pair creation in time-dependent electric fields as well as the reflection above a barrier in one-dimensional Schrodinger quantum mechanics on the other hand is described. This analogy is taken as the basis for the transcription of exact results and for the transcription of a WKB approximation method which allows an easy calculation of the relative probability of cosmological pair creation. For time-symmetric contraction-expansion behaviour the latter can be reduced to a real quadrature. Apart from the mathematical conditions for the application of the approximation procedure, the coherent calculation demands as an additional physical condition that the Cauchy hypersurfaces takes as the in-and out-regions admit free WKB particles. This implies conditions for the metric which are discussed in detail. Generalisations to other cosmologies and other particle equations are indicated.