Does inflation necessarily imply Ω=1?

It is usually stated that, if a universe undergoes a period of significant exponential expansion ('inflation'), then necessarily at the present time we live in a high-density universe with the density parameter Omega very close to the critical value of 1. However, this is not necessarily so; there exist inflationary universes leading to any desired value whatever for the present-day value of Omega , and which furthermore also solve both the horizon and monopole problems. Thus inflation is compatible both with very high-density and with very low-density universes. Furthermore, different approaches to looking at the probability of inflationary universe models suggest it may not even be particularly probable that inflation leads to a universe which is presently near the critical density.