The no-boundary wave function and the duration of the inflationary period

For the simplest minisuperspace model based on a homogeneous, isotropic metric and a minimally coupled scalar field we derive analytic expressions for the caustic which separates Euclidean and Minkowskian region and its breakdown value f∗. This value represents the prediction of the no-boundary wave function for the scalar field at the begining of inflation. We use our results to search for inflationary models which can render the no-boundary wave function consistent with the requirement of a sufficiently long inflationary period.