Quantum cosmology of (loop) quantum gravity condensates: an example

Gielen, Steffen

Abstract

Spatially homogeneous universes can be described in (loop) quantum gravity as condensates of elementary excitations of space. Their treatment is easiest in the second-quantized group field theory formalism, which allows the adaptation of techniques from the description of Bose–Einstein condensates in condensed matter physics. Dynamical equations for the states can be derived directly from the underlying quantum gravity dynamics. The analogue of the Gross–Pitaevskii equation defines an anisotropic quantum cosmology model, in which the condensate wavefunction becomes a quantum cosmology wavefunction on minisuperspace. To illustrate this general formalism, we give a mapping of the gauge-invariant geometric data for a tetrahedron to a minisuperspace of homogeneous anisotropic three-metrics. We then study an example for which we give the resulting quantum cosmology model in the general anisotropic case and derive the general analytical solution for isotropic universes. We discuss the interpretation of these solutions. We suggest that the WKB approximation used in previous studies, corresponding to semiclassical fundamental degrees of freedom of quantum geometry, should be replaced by a notion of semiclassicality that refers to large-scale observables instead.

Citation

Gielen, S. (2014). Quantum cosmology of (loop) quantum gravity condensates: an example. Classical and Quantum Gravity, 31(15), Article 155009. https://doi.org/10.1088/0264-9381/31/15/155009

• Journal Article Type: Article
• Acceptance Date: Jun 17, 2014
• Online Publication Date: Jul 22, 2014
• Publication Date: Aug 7, 2014
• Deposit Date: Oct 22, 2018
• Publicly Available Date: Oct 23, 2018
• Journal: Classical and Quantum Gravity
• Print ISSN: 0264-9381
• Electronic ISSN: 1361-6382
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 31
• Issue: 15
• Article Number: 155009
• DOI: https://doi.org/10.1088/0264-9381/31/15/155009
• Public URL: https://nottingham-repository.worktribe.com/output/1179482
• Publisher URL: http://iopscience.iop.org/article/10.1088/0264-9381/31/15/155009
• Contract Date: Oct 22, 2018