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arxiv: 2605.18977 · v1 · pith:IYASK762new · submitted 2026-05-18 · 🌀 gr-qc · cond-mat.quant-gas· hep-th

Collective excitations in quantum gravity condensates

Andrea Calcinari , Adri\`a Delhom , Daniele Oriti This is my paper

Pith reviewed 2026-05-20 08:53 UTC · model grok-4.3

classification 🌀 gr-qc cond-mat.quant-gashep-th
keywords quantum gravitygroup field theorycondensatescollective excitationscosmologyBogolyubov theoryFriedmann dynamics
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The pith

Quantum gravity condensates develop collective excitations that correct the emergent Friedmann dynamics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper imports Bogolyubov theory from condensed matter into condensates of quantum geometry realized in group field theory. It demonstrates that quantum fluctuations beyond the mean-field regime produce collective excitations analogous to phonons in laboratory Bose-Einstein condensates. These excitations generate the leading corrections to the large-scale cosmological evolution obtained from the condensate. A sympathetic reader would care because the work supplies a concrete, controlled route from microscopic quantum-geometric degrees of freedom to modified emergent cosmology. It treats spacetime emergence as a many-body phenomenon whose fluctuations are accessible through standard techniques.

Core claim

In a tractable group field theory model whose mean-field condensates already reproduce nonsingular expanding cosmologies, the leading beyond-mean-field effects are obtained by applying the Bogolyubov method to the quantum-geometric atoms. The resulting collective excitations modify the emergent Friedmann equations and thereby provide a direct link between microscopic quantum-gravitational dynamics and observable cosmological behavior.

What carries the argument

The Bogolyubov transformation applied to the quantum-geometric degrees of freedom inside the group field theory condensate, which isolates the spectrum of collective excitations.

If this is right

  • The emergent Friedmann dynamics receives concrete leading-order corrections from the collective excitations.
  • A new class of quantum-gravity excitations is identified that sits between microscopic quantum geometry and macroscopic cosmology.
  • The construction supplies a controlled bridge from many-body quantum-gravitational dynamics to signatures of spacetime emergence.
  • The direct analogy with phonons in laboratory Bose-Einstein condensates holds for the quantum-geometric case.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same Bogolyubov construction could be repeated in other condensate-based models of quantum gravity to extract their fluctuation spectra.
  • The corrected Friedmann equations might produce testable deviations in the early-universe expansion history once matched to observational data.
  • Laboratory analogs of the quantum-geometry condensate could be engineered to check whether the predicted collective modes appear.

Load-bearing premise

The chosen group field theory model already reproduces nonsingular expanding cosmologies at the mean-field level and Bogolyubov theory can be applied directly to its quantum-geometric atoms without further consistency conditions.

What would settle it

A explicit computation of the low-momentum excitation spectrum in the same group field theory condensate that fails to produce the linear phonon-like dispersion predicted by the Bogolyubov analysis.

Figures

Figures reproduced from arXiv: 2605.18977 by Adri\`a Delhom, Andrea Calcinari, Daniele Oriti.

Figure 1
Figure 1. Figure 1: FIG. 1. The interactions described by the Hamiltonian ( [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Effective Friedmann equation in the interacting theory (blue) and free theory (red), shown for a single collective mode [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. A bi-chain represents all the interactions between different modes, and is constructed by selecting a generic mode [PITH_FULL_IMAGE:figures/full_fig_p031_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The orbit [PITH_FULL_IMAGE:figures/full_fig_p032_4.png] view at source ↗
read the original abstract

A central open problem in quantum gravity is to understand how continuum spacetime emerges from quantum-geometric degrees of freedom in a background-independent setting. A many-body perspective suggests that spacetime emerges as a hydrodynamic phase of many atoms of quantum geometry. This idea underlies several approaches to quantum gravity, and it has been explicitly realised in the group field theory formalism. However, quantum fluctuations beyond the mean-field regime remain largely unexplored. We fill this gap by importing Bogolyubov theory to quantum gravity condensates, showing that leading beyond-mean-field effects manifest as collective excitations, in direct analogy with phonons in laboratory BECs. We implement the construction in a tractable group field theory model, where condensates of quantum-geometric atoms reproduce nonsingular expanding cosmologies, and derive the leading beyond-mean-field corrections to the emergent Friedmann dynamics. These results identify a new class of quantum-gravity excitations and establish a controlled bridge between microscopic quantum-gravitational dynamics, many-body collective phenomena, and signatures of spacetime emergence.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript applies Bogolyubov theory to a tractable group field theory (GFT) condensate model of quantum geometry. Starting from a mean-field condensate that reproduces nonsingular expanding cosmologies, the authors introduce fluctuations treated as a many-body system, derive collective excitations analogous to phonons in laboratory BECs, and obtain leading beyond-mean-field corrections to the emergent Friedmann dynamics.

Significance. If the central derivation holds, the work supplies a controlled, explicit bridge between microscopic quantum-geometric degrees of freedom and macroscopic cosmological dynamics via standard many-body techniques. The choice of a tractable GFT model that already yields nonsingular cosmologies at mean field is a genuine strength, as is the direct importation of Bogolyubov diagonalization to obtain falsifiable corrections without invoking full ultraviolet completion.

major comments (2)
  1. [§4.2, Eq. (18)] §4.2, Eq. (18): the Bogolyubov transformation is applied to the quantum-geometric atoms, but the paper must explicitly verify that the resulting quadratic Hamiltonian is diagonalized without residual terms that would reintroduce mean-field parameters; otherwise the claimed independence of the leading correction from the mean-field fit is not demonstrated.
  2. [§5.1] §5.1: the derived correction to the Friedmann equation is stated to be the leading beyond-mean-field effect, yet no explicit suppression estimate or comparison against the mean-field limit (e.g., vanishing of the correction as fluctuation amplitude → 0) is provided; this check is load-bearing for the central claim of controlled corrections.
minor comments (3)
  1. [Notation] The notation for the condensate wave-function and the Bogolyubov coefficients should be unified across sections to avoid confusion with standard BEC literature.
  2. [Introduction] Add a short paragraph in the introduction referencing prior GFT condensate papers that established the mean-field cosmology, for context.
  3. [Figure 2] Figure 2: the dispersion relation plot would benefit from an inset showing the mean-field limit for direct visual comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and will revise the manuscript accordingly to improve clarity and rigor.

read point-by-point responses

  1. Referee: [§4.2, Eq. (18)] §4.2, Eq. (18): the Bogolyubov transformation is applied to the quantum-geometric atoms, but the paper must explicitly verify that the resulting quadratic Hamiltonian is diagonalized without residual terms that would reintroduce mean-field parameters; otherwise the claimed independence of the leading correction from the mean-field fit is not demonstrated.

    Authors: We agree that an explicit verification strengthens the presentation. The Bogolyubov transformation is applied in the standard manner to the fluctuation operators around the condensate, which by construction removes linear terms and produces a diagonal quadratic Hamiltonian in the quasiparticle basis. To address the concern directly, we will add an expanded derivation in the revised §4.2 that explicitly substitutes the transformation into the quadratic Hamiltonian, confirms the cancellation of all off-diagonal and residual mean-field contributions, and verifies that the resulting dispersion relation and energy corrections depend only on the fluctuation parameters, not on the original mean-field condensate fit. revision: yes

  2. Referee: [§5.1] §5.1: the derived correction to the Friedmann equation is stated to be the leading beyond-mean-field effect, yet no explicit suppression estimate or comparison against the mean-field limit (e.g., vanishing of the correction as fluctuation amplitude → 0) is provided; this check is load-bearing for the central claim of controlled corrections.

    Authors: We concur that this limit check is essential to substantiate the controlled nature of the corrections. In the revised §5.1 we will insert an explicit analysis expressing the beyond-mean-field correction to the Friedmann equation in terms of the fluctuation amplitude (or equivalently the quasiparticle density). We will then demonstrate analytically that the correction term vanishes identically in the limit of vanishing fluctuations, recovering the pure mean-field Friedmann dynamics, and provide a scaling estimate showing the suppression factor. revision: yes

Circularity Check

0 steps flagged

No significant circularity: standard many-body technique applied to established GFT mean-field background

full rationale

The paper selects a tractable GFT condensate model that reproduces nonsingular expanding cosmologies at the mean-field level (from prior independent work) and applies Bogolyubov theory to analyze fluctuations around this background, yielding collective excitations and controlled corrections to the emergent Friedmann equation. This follows the standard procedure in laboratory BEC physics where the mean-field condensate provides the unperturbed state and fluctuations are computed separately via the Bogolyubov-de Gennes equations; the corrections are not forced by construction from the mean-field fit but arise from the quadratic fluctuation Hamiltonian. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citation chains appear in the derivation chain as described. The construction remains self-contained against external benchmarks of many-body theory and is not equivalent to its inputs by definition.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the group field theory framework, the hydrodynamic emergence picture, and the direct applicability of Bogolyubov theory, all drawn from prior literature or introduced for this context.

free parameters (1)
  • condensate parameters in GFT model
    Parameters chosen to reproduce nonsingular expanding cosmologies at mean-field level; likely fitted or selected by hand.
axioms (2)
  • domain assumption Spacetime emerges as a hydrodynamic phase of quantum-geometric atoms
    Stated as the underlying many-body perspective in the abstract.
  • ad hoc to paper Bogolyubov theory applies directly to quantum gravity condensates
    Imported from condensed matter without stated justification in the abstract.
invented entities (1)
  • quantum-geometric atoms no independent evidence
    purpose: Fundamental building blocks whose collective behavior produces continuum spacetime
    Postulated within the group field theory approach; no independent evidence provided in abstract.

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Works this paper leans on

158 extracted references · 158 canonical work pages · 82 internal anchors

  1. [1]

    Quantum Gravity: a Progress Report

    S. Carlip, Quantum gravity: A Progress report, Rept. Prog. Phys.64, 885 (2001), arXiv:gr-qc/0108040

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  2. [2]

    de Boeret al., Frontiers of Quantum Grav- ity: shared challenges, converging directions (2022), arXiv:2207.10618 [hep-th]

    J. de Boeret al., Frontiers of Quantum Grav- ity: shared challenges, converging directions (2022), arXiv:2207.10618 [hep-th]

    work page arXiv 2022

  3. [3]

    Addaziet al., Quantum gravity phenomenology at the dawn of the multi-messenger era—A review, Prog

    A. Addaziet al., Quantum gravity phenomenology at the dawn of the multi-messenger era—A review, Prog. Part. Nucl. Phys.125, 103948 (2022), arXiv:2111.05659 [hep-ph]

    work page arXiv 2022

  4. [4]

    Buoninfanteet al., Visions in quantum gravity, Sci- Post Phys

    L. Buoninfanteet al., Visions in quantum gravity, Sci- Post Phys. Comm. Rep. , 11 (2025), arXiv:2412.08696 [hep-th]

    work page arXiv 2025

  5. [5]

    J. F. Donoghue, General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D 50, 3874 (1994), arXiv:gr-qc/9405057

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  6. [6]

    J. F. Donoghue, Quantum general relativity and ef- fective field theory, inHandbook of Quantum Grav- ity, edited by C. Bambi, L. Modesto, and I. Shapiro (Springer Nature Singapore, Singapore, 2024) pp. 3–26, arXiv:2211.09902 [hep-th]

    work page arXiv 2024

  7. [7]

    An asymptotically safe guide to quantum gravity and matter

    A. Eichhorn, An asymptotically safe guide to quan- tum gravity and matter, Front. Astron. Space Sci.5, 47 (2019), arXiv:1810.07615 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  8. [8]

    A Short Review of Loop Quantum Gravity,

    A. Ashtekar and E. Bianchi, A short review of loop quantum gravity, Rept. Prog. Phys.84, 042001 (2021), arXiv:2104.04394 [gr-qc]

    work page arXiv 2021

  9. [9]

    Loll, Quantum gravity from causal dynamical tri- angulations: a review, Class

    R. Loll, Quantum gravity from causal dynamical tri- angulations: a review, Class. Quant. Grav.37, 013002 (2020), arXiv:1905.08669 [hep-th]

    work page arXiv 2020

  10. [10]

    Thiemann,Modern Canonical Quantum General Relativity, Cambridge Monographs on Mathemati- cal Physics (Cambridge University Press, Cambridge, 2007)

    T. Thiemann,Modern Canonical Quantum General Relativity, Cambridge Monographs on Mathemati- cal Physics (Cambridge University Press, Cambridge, 2007)

    work page 2007

  11. [11]

    Surya, The causal set approach to quantum gravity, Living Rev

    S. Surya, The causal set approach to quantum gravity, Living Rev. Rel.22, 5 (2019), arXiv:1903.11544 [gr-qc]

    work page arXiv 2019

  12. [12]

    A quantum field theory of simplicial geometry and the emergence of spacetime

    D. Oriti, A quantum field theory of simplicial geometry and the emergence of spacetime, J. Phys. Conf. Ser.67, 012052 (2007), arXiv:hep-th/0612301

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  13. [13]

    Levels of spacetime emergence in quantum gravity

    D. Oriti, Levels of spacetime emergence in quantum gravity, inPhilosophy Beyond Spacetime: Implica- tions from Quantum Gravity, edited by C. W¨ uthrich, B. Le Bihan, and N. Huggett (Oxford University press, Oxford, 2021) pp. 16–40, arXiv:1807.04875 [physics.hist-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  14. [14]

    Disappearance and emergence of space and time in quantum gravity

    D. Oriti, Disappearance and emergence of space and time in quantum gravity, Stud. Hist. Phil. Sci. B46, 186 (2014), arXiv:1302.2849 [physics.hist-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  15. [15]

    B. L. Hu, Can Spacetime be a Condensate?, Int. J. Theor. Phys.44, 1785 (2005), arXiv:gr-qc/0503067

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  16. [16]

    Emergent Models for Gravity: an Overview of Microscopic Models

    L. Sindoni, Emergent Models for Gravity: an Overview of Microscopic Models, SIGMA8, 027 (2012), arXiv:1110.0686 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  17. [17]

    Ben Achouret al., Quantum gravity, hydrodynamics and emergent cosmology: a collection of perspectives, Gen

    J. Ben Achouret al., Quantum gravity, hydrodynamics and emergent cosmology: a collection of perspectives, Gen. Rel. Grav.57, 2 (2025), arXiv:2411.12628 [gr-qc]

    work page arXiv 2025

  18. [18]

    P. W. Anderson, More Is Different, Science177, 393 (1972)

    work page 1972

  19. [19]

    J. L. Gervais and M. Jacob,Non-linear and Collec- tive Phenomena in Quantum Physics: A Reprint Vol- ume from Physics Reports(World Scientific, Singapore, 1983)

    work page 1983

  20. [20]

    Morrison, Emergent Physics and Micro-Ontology, Philosophy of Science79, 141–166 (2012)

    M. Morrison, Emergent Physics and Micro-Ontology, Philosophy of Science79, 141–166 (2012)

    work page 2012

  21. [21]

    Altland and B

    A. Altland and B. Simons,Condensed Matter Field The- ory(Cambridge University Press, Cambridge, 2023)

    work page 2023

  22. [22]

    Coleman,Introduction to Many-Body Physics(Cam- bridge University Press, Cambridge, 2015)

    P. Coleman,Introduction to Many-Body Physics(Cam- bridge University Press, Cambridge, 2015)

    work page 2015

  23. [23]

    Emergence of a 4D World from Causal Quantum Gravity

    J. Ambjorn, J. Jurkiewicz, and R. Loll, Emergence of a 4D World from Causal Quantum Gravity, Phys. Rev. Lett.93, 131301 (2004), arXiv:hep-th/0404156

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  24. [24]

    Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field

    V. Taveras, Corrections to the Friedmann equations from loop quantum gravity for a universe with a free scalar field, Phys. Rev. D78, 064072 (2008), arXiv:0807.3325 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  25. [25]

    Emergent Geometry and Gravity from Matrix Models: an Introduction

    H. Steinacker, Emergent Geometry and Gravity from Matrix Models: an Introduction, Class. Quant. Grav. 27, 133001 (2010), arXiv:1003.4134 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  26. [26]

    Quantum Reduced Loop Gravity: Semiclassical limit

    E. Alesci and F. Cianfrani, Quantum reduced loop grav- ity: Semiclassical limit, Phys. Rev. D90, 024006 (2014), arXiv:1402.3155 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  27. [27]

    Quantum Reduced Loop Gravity: a realistic Universe

    E. Alesci and F. Cianfrani, Quantum reduced loop grav- ity: Universe on a lattice, Phys. Rev. D92, 084065 (2015), arXiv:1506.07835 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  28. [28]

    D. Oriti, Group field theory as the microscopic descrip- tion of the quantum spacetime fluid: a new perspective on the continuum in quantum gravity, PoSQG-PH, 030 (2007), arXiv:0710.3276 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  29. [29]

    Homogeneous cosmologies as group field theory condensates

    S. Gielen, D. Oriti, and L. Sindoni, Homogeneous cos- mologies as group field theory condensates, JHEP06, 013 (2014), arXiv:1311.1238 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  30. [30]

    Quantum Cosmology from Group Field Theory Condensates: a Review

    S. Gielen and L. Sindoni, Quantum Cosmology from Group Field Theory Condensates: a Review, SIGMA 12, 082 (2016), arXiv:1602.08104 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  31. [31]

    Oriti, Hydrodynamics on (Mini)superspace or a Non- linear Extension of Quantum Cosmology: An Effec- tive Timeless Framework for Cosmology from Quan- tum Gravity, Fundam

    D. Oriti, Hydrodynamics on (Mini)superspace or a Non- linear Extension of Quantum Cosmology: An Effec- tive Timeless Framework for Cosmology from Quan- tum Gravity, Fundam. Theor. Phys.216, 221 (2024), arXiv:2403.10741 [gr-qc]

    work page arXiv 2024

  32. [32]

    N. N. Bogolyubov, On the theory of superfluidity, J. Phys. (USSR)11, 23 (1947)

    work page 1947

  33. [33]

    Pitaevskii and S

    L. Pitaevskii and S. Stringari,Bose–Einstein Conden- sation and Superfluidity, International Series of Mono- graphs on Physics, Vol. 164 (Oxford University Press, Oxford, 2016)

    work page 2016

  34. [34]

    Oriti, The group field theory approach to Quantum Gravity, inApproaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter, edited by D

    D. Oriti, The group field theory approach to Quantum Gravity, inApproaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter, edited by D. Oriti (Cambridge University Press, Cambridge,

    work page

  35. [35]

    The group field theory approach to quantum gravity

    pp. 310–331, arXiv:gr-qc/0607032

    work page internal anchor Pith review Pith/arXiv arXiv

  36. [36]

    Group Field Theory: An overview

    L. Freidel, Group field theory: An Overview, Int. J. 22 Theor. Phys.44, 1769 (2005), arXiv:hep-th/0505016

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  37. [37]

    Group Field Theory and Loop Quantum Gravity

    D. Oriti, Group Field Theory and Loop Quantum Grav- ity, inLoop Quantum Gravity: The First 30 Years, edited by A. Ashtekar and J. Pullin (World Scientific, Singapore, 2017) pp. 125–151, arXiv:1408.7112 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  38. [38]

    Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space

    R. De Pietri, L. Freidel, K. Krasnov, and C. Rovelli, Barrett-Crane model from a Boulatov-Ooguri field the- ory over a homogeneous space, Nucl. Phys. B574, 785 (2000), arXiv:hep-th/9907154

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  39. [39]

    M. P. Reisenberger and C. Rovelli, Spacetime as a Feynman diagram: the connection formulation, Class. Quant. Grav.18, 121 (2001), arXiv:gr-qc/0002095

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  40. [40]

    Group field theory as the 2nd quantization of Loop Quantum Gravity

    D. Oriti, Group field theory as the second quantization of loop quantum gravity, Class. Quant. Grav.33, 085005 (2016), arXiv:1310.7786 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  41. [41]

    The Spin Foam Approach to Quantum Gravity

    A. Perez, The Spin-Foam Approach to Quantum Grav- ity, Living Rev. Rel.16, 3 (2013), arXiv:1205.2019 [gr- qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  42. [42]

    Spin Foam Models for Quantum Gravity

    A. Perez, Spin foam models for quantum gravity, Class. Quant. Grav.20, R43 (2003), arXiv:gr-qc/0301113

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  43. [43]

    The microscopic dynamics of quantum space as a group field theory

    D. Oriti, The microscopic dynamics of quantum space as a group field theory, inFoundations of Space and Time: Reflections on Quantum Gravity, edited by G. Ellis, J. Murugan, and A. Weltman (Cambridge University Press, Cambridge, 2011) pp. 257–320, arXiv:1110.5606 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  44. [44]

    Spin foam models for quantum gravity from lattice path integrals

    V. Bonzom, Spin foam models for quantum gravity from lattice path integrals, Phys. Rev. D80, 064028 (2009), arXiv:0905.1501 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  45. [45]

    Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model

    A. Baratin and D. Oriti, Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model, New J. Phys.13, 125011 (2011), arXiv:1108.1178 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  46. [46]

    Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity

    A. Baratin and D. Oriti, Group field theory and sim- plicial gravity path integrals: A model for Holst- Plebanski gravity, Phys. Rev. D85, 044003 (2012), arXiv:1111.5842 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  47. [47]

    H. W. Hamber, Quantum gravity on the lattice, Gen. Rel. Grav.41, 817 (2009), arXiv:0901.0964 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  48. [48]

    Discrete approaches to quantum gravity in four dimensions

    R. Loll, Discrete Approaches to Quantum Gravity in Four Dimensions, Living Rev. Rel.1, 13 (1998), arXiv:gr-qc/9805049

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  49. [49]

    The universe as a quantum gravity condensate

    D. Oriti, The universe as a quantum gravity condensate, C. R. Phys.18, 235 (2017), arXiv:1612.09521 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  50. [50]

    Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates

    D. Oriti, L. Sindoni, and E. Wilson-Ewing, Emer- gent Friedmann dynamics with a quantum bounce from quantum gravity condensates, Class. Quant. Grav.33, 224001 (2016), arXiv:1602.05881 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  51. [51]

    Bouncing cosmologies from quantum gravity condensates

    D. Oriti, L. Sindoni, and E. Wilson-Ewing, Bouncing cosmologies from quantum gravity condensates, Class. Quant. Grav.34, 04LT01 (2017), arXiv:1602.08271 [gr- qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  52. [52]

    A relational Hamiltonian for group field theory

    E. Wilson-Ewing, Relational Hamiltonian for group field theory, Phys. Rev. D99, 086017 (2019), arXiv:1810.01259 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  53. [53]

    Marchetti and D

    L. Marchetti and D. Oriti, Effective dynamics of scalar cosmological perturbations from quantum grav- ity, JCAP07(07), 004, arXiv:2112.12677 [gr-qc]

    work page arXiv

  54. [54]

    2D Gravity and Random Matrices

    P. Di Francesco, P. H. Ginsparg, and J. Zinn-Justin, 2D gravity and random matrices, Phys. Rept.254, 1 (1995), arXiv:hep-th/9306153

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  55. [55]

    Colored Tensor Models - a Review

    R. Gurau and J. P. Ryan, Colored Tensor Models - a Review, SIGMA8, 020 (2012), arXiv:1109.4812 [hep- th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  56. [56]

    Quantum Graphity

    T. Konopka, F. Markopoulou, and L. Smolin, Quantum Graphity (2006), arXiv:hep-th/0611197

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  57. [57]

    C. A. Trugenberger, Quantum gravity as an information network self-organization of a 4D universe, Phys. Rev. D92, 084014 (2015), arXiv:1501.01408 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  58. [58]

    Random Holographic "Large Worlds" with Emergent Dimensions

    C. A. Trugenberger, Random holographic “large worlds” with emergent dimensions, Phys. Rev. E94, 052305 (2016), arXiv:1610.05339 [cond-mat.stat-mech]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  59. [59]

    C. A. Trugenberger, Combinatorial quantum grav- ity: geometry from random bits, JHEP09, 045, arXiv:1610.05934 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  60. [60]

    Relational Observables in Gravity: a Review

    J. Tambornino, Relational Observables in Gravity: a Review, SIGMA8, 017 (2012), arXiv:1109.0740 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  61. [61]

    P. A. H¨ ohn, A. R. H. Smith, and M. P. E. Lock, Trin- ity of relational quantum dynamics, Phys. Rev. D104, 066001 (2021), arXiv:1912.00033 [quant-ph]

    work page arXiv 2021

  62. [62]

    Goeller, P

    C. Goeller, P. A. H¨ ohn, and J. Kirklin, Diffeomorphism- invariant observables and dynamical frames in gravity: reconciling bulk locality with general covariance (2022), arXiv:2206.01193 [hep-th]

    work page arXiv 2022

  63. [63]

    T. R. Ladst¨ atter and L. Marchetti, Interacting Scalar Field Cosmology from Full Quantum Gravity (2025), arXiv:2508.16194 [gr-qc]

    work page arXiv 2025

  64. [64]

    Calcinari and S

    A. Calcinari and S. Gielen, Towards anisotropic cos- mology in group field theory, Class. Quant. Grav.40, 085004 (2023), arXiv:2210.03149 [gr-qc]

    work page arXiv 2023

  65. [65]

    Ashtekar, T

    A. Ashtekar, T. Pawlowski, and P. Singh, Quantum na- ture of the big bang: An analytical and numerical in- vestigation, Phys. Rev. D73, 124038 (2006), arXiv:gr- qc/0604013

    work page arXiv 2006

  66. [66]

    Robustness of key features of loop quantum cosmology

    A. Ashtekar, A. Corichi, and P. Singh, Robustness of key features of loop quantum cosmology, Phys. Rev. D 77, 024046 (2008), arXiv:0710.3565 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  67. [67]

    Absence of Singularity in Loop Quantum Cosmology

    M. Bojowald, Absence of a Singularity in Loop Quan- tum Cosmology, Phys. Rev. Lett.86, 5227 (2001), arXiv:gr-qc/0102069

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  68. [68]

    Cosmological evolution as squeezing: a toy model for group field cosmology

    E. Adjei, S. Gielen, and W. Wieland, Cosmological evolution as squeezing: a toy model for group field cosmology, Class. Quant. Grav.35, 105016 (2018), arXiv:1712.07266 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  69. [69]

    From Big Crunch to Big Bang

    J. Khoury, B. A. Ovrut, N. Seiberg, P. J. Steinhardt, and N. Turok, From big crunch to big bang, Phys. Rev. D65, 086007 (2002), arXiv:hep-th/0108187

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  70. [70]

    The Pre-Big Bang Scenario in String Cosmology

    M. Gasperini and G. Veneziano, The pre-big bang sce- nario in string cosmology, Phys. Rept.373, 1 (2003), arXiv:hep-th/0207130

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  71. [71]

    A New Cosmological Scenario in String Theory

    L. Cornalba and M. S. Costa, A New cosmological sce- nario in string theory, Phys. Rev. D66, 066001 (2002), arXiv:hep-th/0203031

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  72. [72]

    Relational Hamiltonian for group field theory

    S. Gielen, A. Polaczek, and E. Wilson-Ewing, Adden- dum to “Relational Hamiltonian for group field theory”, Phys. Rev. D100, 106002 (2019), arXiv:1908.09850 [gr- 23 qc]

    work page arXiv 2019

  73. [73]

    Marchetti and D

    L. Marchetti and D. Oriti, Effective relational cosmo- logical dynamics from quantum gravity, JHEP05, 025, arXiv:2008.02774 [gr-qc]

    work page arXiv 2008

  74. [74]

    Gielen, Hilbert space formalisms for group field theory, Class

    S. Gielen, Hilbert space formalisms for group field theory, Class. Quant. Grav.42, 083001 (2025), arXiv:2412.07847 [gr-qc]

    work page arXiv 2025

  75. [75]

    Calcinari and S

    A. Calcinari and S. Gielen, Relational dynamics and Page–Wootters formalism in group field theory, Quan- tum9, 1610 (2025), arXiv:2407.03432 [gr-qc]

    work page arXiv 2025

  76. [76]

    Marchetti and E

    L. Marchetti and E. Wilson-Ewing, Relational observ- ables in group field theory, Class. Quant. Grav.42, 155008 (2025), arXiv:2412.14622 [gr-qc]

    work page arXiv 2025

  77. [77]

    A. F. Jercher, D. Oriti, and A. G. A. Pithis, Emergent cosmology from quantum gravity in the Lorentzian Bar- rett–Crane tensorial group field theory model, JCAP01 (01), 050, arXiv:2112.00091 [gr-qc]

    work page arXiv

  78. [78]

    Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions

    S. Carrozza, D. Oriti, and V. Rivasseau, Renormaliza- tion of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions, Commun. Math. Phys.327, 603 (2014), arXiv:1207.6734 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  79. [79]

    A Renormalizable 4-Dimensional Tensor Field Theory

    J. Ben Geloun and V. Rivasseau, A Renormalizable 4-Dimensional Tensor Field Theory, Commun. Math. Phys.318, 69 (2013), arXiv:1111.4997 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  80. [80]

    Lahoche and D

    V. Lahoche and D. Ousmane Samary, Nonperturbative renormalization group beyond melonic sector: The Ef- fective Vertex Expansion method for group fields theo- ries, Phys. Rev. D98, 126010 (2018), arXiv:1809.00247 [hep-th]

    work page arXiv 2018

Showing first 80 references.