The evolution of Ω in inflationary universes

Phase-plane diagrams are presented showing the evolution of the cosmological density parameter Ω in terms of the Robertson-Walker scale factor S. These diagrams are given for both simple fluids and for mixtures of fluids; this enables construction of such diagrams for inflationary universes, whether the inflation is exponential or power-law inflation. The diagrams enable simple consideration of the evolution of the density parameter in inflationary universe models, and clearly demonstrate that there exist such models leading to any value whatever for Ω at the present day. (author)