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Cited by 43Noncommutative and Quantum Gravity TheoriesCosmology and Gravitation TheoriesRelativity and Gravitational Theory

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

Open access
Gielen, Steffen·2014·Classical and Quantum Gravity
DOI 10.1088/0264-9381/31/15/155009
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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-quantised 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 3-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.

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  • The effective hydrodynamics of GFT condensates can be turned into an effective Hamiltonian constraint equation acting on the condensate wavefunction, but this is only possible for the free part of the dynamics.

    “The effective hydrodynamics of GFT condensates can be turned in the form of an effective Hamiltonian constraint equation acting on the condensate wavefunction, from which one can try to read out the relation with gravitational dynamics and the Friedmann equations.”

    From The universe as a quantum gravity condensate (2017) · cites this paper as [24]

    The Introduction (p. 4) says GFT dynamical constraints can be translated into equations for the condensate wavefunction, supporting the effective-constraint part of the claim. Section 2 (pp. 7–8) includes both kinetic and potential terms and says the resulting equations are generally nonlinear; it does not support the added assertion that this is possible only for the free part of the dynamics. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • The effective dynamics obtained from the Schwinger-Dyson equations with the condensate state is the analog of the Gross-Pitaevskii equation for real Bose condensates.

    “When the expectation value is taken with respect to the condensate state | σ 〉 , one obtains the analog of the Gross-Pitaevskii (GP) equation for real Bose condensates”

    From Impact of nonlinear effective interactions on group field theory quantum gravity condensates (2016) · cites this paper as [11]

  • The near flatness condition translates into demanding that the character of the group elements decorating the quantum tetrahedra are close to χ(1_{J_i}) = 2J_i+1.

    “In the group representation, this condition concretely translates into demanding that the character of the group elements decorating the quantum tetrahedra are close to χ ( 1 J i ) = 2 J i +1 according to Refs. [4, 11].”

    From Impact of nonlinear effective interactions on group field theory quantum gravity condensates (2016) · cites this paper as [11]

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Research works printed but not linked: 21

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Cited by

Sorted by citations

Authors
Gielen, S.
Corresponding author
Gielen, Steffen
Venue
Classical and Quantum Gravity
Publisher
IOP Publishing
Published
2014-07-22
Volume
31
Issue
15
Pages
155009
ISSN
  • 0264-9381 (ISSN-L)
  • 1361-6382
DOI
10.1088/0264-9381/31/15/155009
OpenAlex
W2042693453
Cited by
43
References
7
Citations by year
2025: 1 · 2024: 3 · 2023: 1 · 2022: 7 · 2021: 4 · 2020: 1 · 2019: 1 · 2018: 3 · 2017: 6 · 2016: 7 · 2015: 7 · 2014: 2
FWCI
4.83
Type
journal article
Language
en
Open access
Licence
Locations
  • Classical and Quantum Gravity (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • Repository@Nottingham (University of Nottingham) (acceptedVersion, other-oa)
  • Repository@Nottingham (University of Nottingham) (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
  • Government of Canada
  • Industry Canada
  • Institut Périmètre de physique théorique
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
loop quantum gravity, quantum cosmology, group field theory, Bose-Einstein condensate, Gross-Pitaevskii equation, minisuperspace, anisotropic cosmology, tetrahedron, isotropic universe, WKB approximation, quantum geometry

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