Homogeneous cosmologies as group field theory condensates
Open accessAbstract
We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the ‘condensate wavefunction’ which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.
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A Friedmann-like evolution equation can be derived from the effective dynamics of specific GFT condensates.
“We refer to Refs. [4, 5, 7, 8, 10], where it has been demonstrated how a Friedmann-like evolution equation can be derived from such an effective dynamics of specific GFT condensates.”
From Impact of nonlinear effective interactions on group field theory quantum gravity condensates (2016) · cites this paper as [10]
A bounded interaction potential generically leads to recollapsing condensate solutions.
“This behavior is reminiscent of the effect of similar interactions onto the effective curvature of the space described by the condensate in Ref. [10], where it was shown that a bounded interaction potential generically leads to recollapsing condensate solutions.”
From Impact of nonlinear effective interactions on group field theory quantum gravity condensates (2016) · cites this paper as [10]
Relationally evolving and effectively interacting GFTCC models display recollapsing solutions when the interaction potential is bounded from below.
“This is again reminiscent of similar findings in Ref. [10] where it was shown that relationally evolving and effectively interacting GFTCC models display recollapsing solutions when the interaction potential is bounded from below as here.”
From Impact of nonlinear effective interactions on group field theory quantum gravity condensates (2016) · cites this paper as [10]
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- Authors
- Gielen, S., Oriti, D., & Sindoni, L.
- Affiliations
- Max Planck Society (DE)
- Corresponding author
- Gielen, Steffen
- Venue
- Journal of High Energy Physics
- Published
- 2014-06
- Volume
- 2014
- Issue
- 6
- ISSN
- 1029-8479 (ISSN-L)
- OpenAlex
- W2069490110
- Cited by
- 159
- References
- 18
- Citations by year
- 2026: 5 · 2025: 8 · 2024: 11 · 2023: 12 · 2022: 12 · 2021: 11 · 2020: 11 · 2019: 13 · 2018: 14 · 2017: 18 · 2016: 19 · 2015: 18 · 2014: 6 · 2012: 1
- FWCI
- 13.39
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- cc-by
- Locations
- Journal of High Energy Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (publishedVersion)
- Repository@Nottingham (University of Nottingham) (publishedVersion, cc-by)
- White Rose Research Online (University of Leeds, The University of Sheffield, University of York) (acceptedVersion)
- Repository@Nottingham (University of Nottingham) (submittedVersion, cc-by)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Government of Canada
- Industry Canada
- Institut Périmètre de physique théorique
- Agencia Estatal de Investigación
- 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
- group field theory, quantum gravity, spatially homogeneous cosmology, coherent states, Gross-Pitaevskii equation, Wheeler-DeWitt equation, WKB approximation, Friedmann equations, Lorentzian signature, massless scalar field, cosmological perturbations, non-perturbative quantum gravity
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