Quantum propagation across cosmological singularities

TL;DR

This paper explores quantum cosmology with conformal matter, demonstrating a quantum bounce that allows the universe to transition smoothly through the classical singularity, and analyzes stability and perturbations across this bounce.

Contribution

It provides exact solutions for quantum cosmological models with conformal matter, including anisotropies and inhomogeneities, and introduces a novel approach to resolving the big bang singularity.

Findings

Exact Feynman propagator for FRW backgrounds computed.

Quantum bounce allows universe to evolve through singularity.

No particle production across the bounce at linear and nonlinear levels.

Abstract

The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show it is natural to extend the scale factor to negative values, allowing a large, collapsing Universe to evolve across a quantum "bounce" into an expanding Universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.