Large Universe as the initial condition for a Collapsing Universe

Abstract

Using the extension of the standard Hawking-Hartle prescription for defining a wave function for the universe, we show that it is possible, given a suitable form for the scalar field potential, to have the universe begin at its largest size and thereafter contract, with the growth of perturbations proceeding from small, at the largest size, to largest when the universe is small. This solution would dominate the wave function by an exponentially large amount if one chooses the Hartle Hawking prescription for the wave-function, but is exponentially sub-dominant for the Linde-Vilenkin prescription.