The density parameter and the Anthropic Principle

In the context of open inflation, we calculate the probability distribution for the density parameter Ω. A large class of two field models of open inflation do not lead to infinite open universes, but to an ensemble of inflating islands of finite size, or “quasi-open” universes, where the density parameter takes a range of values. Assuming we are typical observers, the models make definite predictions for the value Ω we are most likely to observe. We also argue that obsevers should not be surprised to find themselves living at the time when curvature is about to dominate.