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Quantum propagation across cosmological singularities

Gielen, Steffen; Turok, Neil


Steffen Gielen

Neil Turok


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.


Gielen, S., & Turok, N. (2017). Quantum propagation across cosmological singularities. Physical Review D, 95(10), Article 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
Public URL
Publisher URL


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