Asymmetric creation of matter and antimatter in the expanding universe

We consider a simple model in which the matter-antimatter asymmetry of the universe is brought about by an effective two-particle interaction that violates baryon-number conservation as well as CP invariance. The particle fields participating in the interaction are quantized, and their time development in an isotropically expanding universe is found to all orders in the coupling constant. Pair production by the asymmetric interaction, as well as symmetric production by the gravitational field of the expanding universe, appear simultaneously in the solution. Taking an initial state in which no particles participating in the asymmetric interaction are present, we find the created baryon-number density. We consider in more detail the case when the matter-antimatter asymmetry is produced during a stage when the radius of the universe is small with respect to its present value. We make numerical estimates of the created matter-antimatter asymmetry, and put limits on possible values of the parameters of this model.