Quantum Creation of an Open Inflationary Universe

We discuss a dramatic difference between the description of the quantum creation of an open universe using the Hartle-Hawking wave function and the tunneling wave function. Recently Hawking and Turok (hep-th/9802030) have found that the Hartle-Hawking wave function leads to a universe with Omega = 0.01, which is much smaller that the observed value of Omega. Galaxies in such a universe would be $10^{10^8}$ light years away from each other, so the universe would be practically structureless. We argue that the Hartle-Hawking wave function does not describe the probability of creation of the universe. If one uses the tunneling wave function for the description of creation of the universe, then in most inflationary models the universe should have Omega = 1, which agrees with the standard expectation that inflation makes the universe flat. However, there exist two classes of models where $\Omega$ may take any value, from Omega > 1 to Omega << 1.