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

Gielen, Steffen


Steffen Gielen


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.


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

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
Public URL
Publisher URL


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