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Homogeneous cosmologies as group field theory condensates

Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo

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Steffen Gielen

Daniele Oriti

Lorenzo Sindoni


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.


Gielen, S., Oriti, D., & Sindoni, L. (2014). Homogeneous cosmologies as group field theory condensates. Journal of High Energy Physics, 2014(6), doi:10.1007/jhep06(2014)013

Journal Article Type Article
Acceptance Date May 1, 2014
Online Publication Date Jun 3, 2014
Publication Date Jun 30, 2014
Deposit Date Oct 22, 2018
Publicly Available Date Oct 22, 2018
Journal Journal of High Energy Physics
Publisher BMC
Peer Reviewed Peer Reviewed
Volume 2014
Issue 6
Article Number 013
Public URL
Publisher URL


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