Large Universe as the initial condition for a Collapsing Universe

TL;DR

This paper explores initial conditions for a collapsing universe using quantum cosmology, showing that specific scalar field potentials can lead to a universe starting at its largest size and contracting, with perturbations evolving accordingly.

Contribution

It demonstrates that under certain scalar field potentials, a universe can begin at maximum size and contract, with implications for quantum cosmological wave functions.

Findings

Collapse solution dominates with Hartle-Hawking prescription

Collapse solution is sub-dominant with Linde-Vilenkin prescription

Perturbations grow from small at largest size to large when small

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.