We propose a mechanism of quantum creation of the open Universe in the obse
rvable range of values of Omega. This mechanism is based on the no-boundary
quantum state with the Hawking-Turok instanton applied to the model with a
strong non-minimal coupling of the inflaton field. We develop the slow rol
l perturbation expansion for the instanton solution and obtain a non-trivia
l contribution to the classical instanton action. The interplay of this cla
ssical contribution with the loop effects due to quantum effective action g
enerates the probability distribution peak with necessary parameters of the
inflation stage without invoking any anthropic considerations. In contrast
with a similar mechanism for closed models, existing only for the tunnelin
g quantum state of the Universe, the observationally justified open inflati
on originates from the no-boundary cosmological wavefunction. (C) 1999 Else
vier Science B.V. All rights reserved.