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 phi*. This value represents the prediction of the no-boundary wave function for the scalar field at the beginning 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.