Density parameter and the anthropic principle - art. no. 023501

In the context of open inflation, we calculate the probability distribution for the density parameter Omega. A large class of two field models of open inflation do not lead to infinite open universes, but to an ensemble of in flating islands of finite size, or "quasi-open'' universes, where the densi ty parameter takes a range of values. Assuming we are typical observers, th e models make definite predictions for the value Omega we are most likely t o observe. When compared with observations, these predictions can be used t o constrain the parameters of the models. We also argue that observers shou ld not be surprised to find themselves living at the time when curvature is about to dominate. [S0556-2821(99)04712-8].