Large Universe as the initial condition for a Collapsing Universe

摘要

Using the extension of the standard Hawking-Hartle prescription for defininga wave function for the universe, we show that it is possible, given a suitableform for the scalar field potential, to have the universe begin at its largestsize and thereafter contract, with the growth of perturbations proceeding fromsmall, at the largest size, to largest when the universe is small. Thissolution would dominate the wave function by an exponentially large amount ifone chooses the Hartle Hawking prescription for the wave-function, but isexponentially sub-dominant for the Linde-Vilenkin prescription.