Quantum propagation across cosmological singularities

Gielen, Steffen; Turok, Neil

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 that 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.

Citation

Gielen, S., & Turok, N. (2017). Quantum propagation across cosmological singularities. Physical Review D, 95(10), Article 103510. https://doi.org/10.1103/physrevd.95.103510

• Journal Article Type: Article
• Acceptance Date: Apr 17, 2017
• Online Publication Date: May 18, 2017
• Publication Date: May 18, 2017
• Deposit Date: Oct 22, 2018
• Publicly Available Date: Oct 22, 2018
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 95
• Issue: 10
• Article Number: 103510
• DOI: https://doi.org/10.1103/physrevd.95.103510
• Public URL: https://nottingham-repository.worktribe.com/output/1179315
• Publisher URL: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.103510
• Contract Date: Oct 22, 2018