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arxiv: 2506.13812 · v2 · submitted 2025-06-14 · ⚛️ physics.gen-ph · gr-qc

Late-Time Cosmic Acceleration from QCD Confinement Dynamics

Jonathan Rinc\'on Saucedo , Humberto Mart\'inez-Huerta , Adolfo Huet , Alberto Hern\'andez-Almada , Miguel A. Garc\'ia-Aspeitia This is my paper

Pith reviewed 2026-05-19 09:29 UTC · model grok-4.3

classification ⚛️ physics.gen-ph gr-qc
keywords QCD confinementlate-time cosmic accelerationPNJL modelPolyakov loop potentialdynamical vacuum energyFLRW cosmologyBayesian constraints
0
0 comments X p. Extension

The pith

A curvature term added to the QCD Polyakov potential generates late-time cosmic acceleration without a fundamental constant.

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

The authors modify the Polyakov-Nambu-Jona-Lasinio model by inserting a term that depends on the Hubble expansion rate into the effective potential for the Polyakov loop. This addition is active only in the confined phase and supplies an effective dynamical vacuum energy that becomes dominant at low redshifts. The construction is tested at the background level in a flat FLRW universe against data from cosmic chronometers, Type Ia supernovae, HII galaxies and quasars. Bayesian fits show the model matches observations at least as well as Lambda CDM while leaving room for small differences. The work therefore links the non-perturbative dynamics of quark confinement directly to the present-day expansion of the universe.

Core claim

In a spatially flat FLRW background the insertion of the term alpha (H/H0)^d f(Phi, Phi*) into the Polyakov loop potential produces a thermodynamically consistent effective pressure that acts as a dynamical vacuum component at late times, vanishes in the deconfined regime, and yields a statistically competitive fit to low-redshift cosmological data sets while permitting mild departures from Lambda CDM.

What carries the argument

The curvature-sensitive term alpha (H/H0)^d f(Phi, Phi*) added to the Polyakov loop potential, which supplies an effective dynamical vacuum energy only in the confined phase.

If this is right

  • The model reproduces the observed late-time acceleration using only parameters tied to QCD confinement.
  • Bayesian constraints on alpha and d are obtained from current low-redshift data sets.
  • The coupling shifts the location of the critical endpoint in the QCD phase diagram.
  • Small deviations from Lambda CDM remain allowed within present observational uncertainties.

Where Pith is reading between the lines

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

  • If the mechanism is correct, the acceleration could be viewed as a macroscopic consequence of confinement dynamics rather than an independent dark-energy component.
  • Future measurements that tighten the expansion history between redshift 0.5 and 2 could determine the exponent d and distinguish this construction from other dynamical-vacuum proposals.
  • The same curvature dependence might be examined in effective models of the early universe or in the interiors of compact stars to check consistency with known QCD phenomenology.

Load-bearing premise

The non-perturbative QCD vacuum in the confined phase retains a residual sensitivity to cosmic expansion that can be modeled by a simple power-law term in the effective potential.

What would settle it

A high-precision measurement of the Hubble parameter at intermediate redshifts that forces the amplitude alpha to be consistent with zero or shows that the model’s predicted expansion history deviates systematically from the data.

Figures

Figures reproduced from arXiv: 2506.13812 by Adolfo Huet, Alberto Hern\'andez-Almada, Humberto Mart\'inez-Huerta, Jonathan Rinc\'on Saucedo, Miguel A. Garc\'ia-Aspeitia.

Figure 1
Figure 1. Figure 1: FIG. 1. 1D posterior distributions and 2D contours at 1 [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Reconstruction of the Hubble parameter (first panel), the deceleration parameter (second panel) for the QCD model [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Chiral condensate and Polyakov loop as a function of temperature for the modified PNJL model. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Maximal chiral susceptibility as a function of the chemical potential for the PNJL model in different configurations: [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Phase diagram in the [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

We explore a phenomenological extension of the Polyakov-Nambu-Jona-Lasinio (PNJL) model by introducing a curvature-sensitive effective contribution to the Polyakov loop potential, motivated by the hypothesis that the non-perturbative QCD vacuum in the confined phase may retain a residual sensitivity to cosmic expansion. In a spatially flat FLRW background, this modification reduces to a term proportional to $\alpha(H/H_0)^d f(\Phi, \Phi^*)$, which naturally vanishes in the deconfined regime and behaves as an effective dynamical vacuum component at late times, without invoking a fundamental cosmological constant. The construction provides an effective thermodynamic description of the QCD sector within an adiabatic framework and introduces a minimal phenomenological extension characterized by the exponent $d$ and the amplitude parameter $\alpha$. We analyze the cosmological implications at the background level and confront the model with low-redshift observations, including cosmic chronometers, Type Ia supernovae, HII galaxies, and quasars. Using Bayesian Monte Carlo techniques, we constrain the model parameters and compare its performance with $\Lambda$CDM. Our results indicate that the modified PNJL cosmology provides a statistically competitive fit to current data while allowing small departures from $\Lambda$CDM within observational uncertainties. We also investigate the impact of the coupling on the QCD phase diagram and the critical end point. The framework offers a tractable effective approach to connect confinement physics with late-time cosmology and suggests directions for further theoretical development in QCD under curved backgrounds.

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 / 2 minor

Summary. The manuscript proposes a phenomenological extension of the Polyakov-Nambu-Jona-Lasinio (PNJL) model in which a curvature-dependent term proportional to α(H/H₀)^d f(Φ, Φ*) is added to the Polyakov-loop potential. In a flat FLRW background this term is stated to vanish in the deconfined phase and to act as an effective dynamical vacuum energy at late times, thereby linking QCD confinement dynamics to late-time cosmic acceleration without a fundamental cosmological constant. The authors constrain the two free parameters α and d via Bayesian Monte Carlo sampling against low-redshift data (cosmic chronometers, Type Ia supernovae, HII galaxies, quasars) and report that the resulting cosmology yields a statistically competitive fit to ΛCDM while permitting only small departures.

Significance. If the added term could be derived from an effective action for QCD in curved spacetime, the construction would supply a concrete bridge between non-perturbative QCD and cosmology. The use of multiple independent low-redshift probes together with Bayesian parameter estimation constitutes a clear methodological strength and yields falsifiable predictions for small deviations from ΛCDM. At present, however, the model remains an effective description whose predictive power is limited by the two additional parameters.

major comments (2)
  1. [Abstract and §2] Abstract and §2 (model definition): the functional form α(H/H₀)^d f(Φ, Φ*) is introduced phenomenologically; no derivation from the QCD action expanded in Riemann tensors, no lattice result in an expanding background, and no effective-field-theory argument is supplied to fix either the exponent d or the explicit dependence of f on the Polyakov loop. This term is load-bearing for the central claim that acceleration emerges from confinement dynamics.
  2. [§4–5] §4–5 (parameter estimation and model comparison): the same low-redshift datasets used to constrain α and d are subsequently employed to assert statistical competitiveness with ΛCDM. Because the two extra parameters are tuned directly to these data, the reported goodness-of-fit is partly by construction and does not yet demonstrate an emergent feature of QCD.
minor comments (2)
  1. [Model section] The explicit functional dependence of f(Φ, Φ*) on the Polyakov loop is stated only in the abstract; a concrete expression or limiting behavior should be written out in the model section for reproducibility.
  2. [Figures and Tables] Figure captions and table headings should explicitly state the priors adopted for α and d and the precise combination of datasets entering each posterior.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [Abstract and §2] Abstract and §2 (model definition): the functional form α(H/H₀)^d f(Φ, Φ*) is introduced phenomenologically; no derivation from the QCD action expanded in Riemann tensors, no lattice result in an expanding background, and no effective-field-theory argument is supplied to fix either the exponent d or the explicit dependence of f on the Polyakov loop. This term is load-bearing for the central claim that acceleration emerges from confinement dynamics.

    Authors: We agree that the proposed term is introduced as a phenomenological extension, as explicitly stated in the manuscript. The functional form is motivated by the physical hypothesis that the confined QCD vacuum may exhibit residual sensitivity to the cosmic curvature scale, leading to an effective contribution that vanishes in the deconfined phase. While a rigorous derivation from the QCD effective action in curved spacetime or from lattice QCD in an expanding background is not available and lies beyond the current scope, we have revised §2 to provide a more detailed thermodynamic justification within the adiabatic approximation and to discuss possible connections to curvature couplings in effective field theories. We have also clarified in the abstract that this is a minimal phenomenological model. This addresses the concern by strengthening the motivation without claiming a first-principles derivation. revision: partial

  2. Referee: [§4–5] §4–5 (parameter estimation and model comparison): the same low-redshift datasets used to constrain α and d are subsequently employed to assert statistical competitiveness with ΛCDM. Because the two extra parameters are tuned directly to these data, the reported goodness-of-fit is partly by construction and does not yet demonstrate an emergent feature of QCD.

    Authors: We acknowledge the validity of this observation. In phenomenological models with additional parameters, fitting to the data is indeed part of the construction. To mitigate this, we have employed Bayesian model comparison using the evidence ratio and AIC/BIC criteria, which account for the extra degrees of freedom. We have revised §5 to explicitly discuss the limitations of the current analysis and to emphasize that the model predicts specific deviations in the QCD phase structure and Polyakov loop evolution that are independent of the low-redshift fit and can be tested with future observations or lattice simulations. This strengthens the claim that the acceleration emerges from the confinement dynamics within the effective framework. revision: yes

standing simulated objections not resolved
  • A first-principles derivation of the specific curvature-dependent term from the QCD action in an expanding background is not provided in the manuscript, as the approach is phenomenological.

Circularity Check

0 steps flagged

No significant circularity: phenomenological extension with explicit parameters fitted to external data

full rationale

The paper describes its key addition as a 'phenomenological extension' and 'minimal phenomenological extension characterized by the exponent d and the amplitude parameter α', motivated by hypothesis rather than derived from first principles or lattice QCD in curved space. The term α(H/H0)^d f(Φ, Φ*) is constructed to vanish in the deconfined phase and act as effective vacuum energy at late times, but this is stated openly as an ansatz for the effective thermodynamic description. Parameters are then constrained via Bayesian Monte Carlo against independent low-redshift datasets (cosmic chronometers, SNe Ia, HII galaxies, quasars) and the model is compared to ΛCDM using standard statistical metrics. No load-bearing self-citation, uniqueness theorem, or reduction of the central claim to a fitted input presented as an independent prediction occurs. The reported competitive fit is the direct outcome of parameter adjustment in a transparent effective model, not a circular derivation from unmodified QCD dynamics.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The construction rests on two fitted parameters and the ad-hoc curvature term; background cosmology and the base PNJL model are taken from prior literature.

free parameters (2)
  • α
    Amplitude of the curvature-sensitive contribution, constrained by observations
  • d
    Exponent that sets the Hubble-rate dependence of the new term
axioms (2)
  • domain assumption Spatially flat FLRW metric
    Standard assumption for late-time cosmology
  • domain assumption Adiabatic thermodynamic description of the QCD sector
    Framework stated in the abstract
invented entities (1)
  • curvature-sensitive effective contribution to the Polyakov loop potential no independent evidence
    purpose: To generate late-time acceleration from QCD confinement without a fundamental cosmological constant
    Introduced phenomenologically; no independent evidence outside the cosmological fit is provided

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Works this paper leans on

52 extracted references · 52 canonical work pages · 7 internal anchors

  1. [1]

    A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, et al. , The Astronomical Journal 116, 1009 (1998)

    work page 1998

  2. [2]

    Perlmutter, G

    S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, others, and T. S. C. Project, The Astrophys- ical Journal 517, 565 (1999)

    work page 1999

  3. [3]

    Y. B. Zeldovich, Soviet Physics Uspekhi 11 (1968)

    work page 1968

  4. [4]

    Weinberg, Reviews of Modern Physics 61 (1989)

    S. Weinberg, Reviews of Modern Physics 61 (1989)

    work page 1989

  5. [5]

    Y. B. Alc´ antara-P´ erez, M. A. Garc´ ıa-Aspeitia, H. Mart´ ınez-Huerta, and A. Hern´ andez-Almada, Universe 9, 513 (2023), arXiv:2309.11659 [astro-ph.CO]

    work page arXiv 2023

  6. [6]

    Li and A

    X. Li and A. Shafieloo, Astrophys. J. 902, 58 (2020), arXiv:2001.05103 [astro-ph.CO]

    work page arXiv 2020

  7. [7]

    H. Koo, A. Shafieloo, R. E. Keeley, and B. L’Huillier, Astrophys. J. 899, 9 (2020), arXiv:2001.10887 [astro- ph.CO]

    work page arXiv 2020

  8. [8]

    Hern´ andez-Almada, M

    A. Hern´ andez-Almada, M. L. Mendoza-Mart´ ınez, M. A. Garc´ ıa-Aspeitia, and V. Motta, Phys. Dark Univ. 46, 101668 (2024), arXiv:2407.09430 [astro-ph.CO]

    work page arXiv 2024

  9. [9]

    Hern´ andez-Almada, G

    A. Hern´ andez-Almada, G. Leon, J. Maga˜ na, M. A. Garc´ ıa-Aspeitia, and V. Motta, Mon. Not. Roy. Astron. Soc. 497, 1590 (2020), arXiv:2002.12881 [astro-ph.CO]

    work page arXiv 2020

  10. [10]

    J. D. Barrow, Phys. Lett. B 808, 135643 (2020), arXiv:2004.09444 [gr-qc]

    work page arXiv 2020

  11. [11]

    E. M. C. Abreu and J. Ananias Neto, EPL 133, 49001 (2021)

    work page 2021

  12. [12]

    Esteban-Guti´ errez, M

    A. Esteban-Guti´ errez, M. A. Garc´ ıa-Aspeitia, A. Hern´ andez-Almada, J. Maga˜ na, and V. Motta, Phys. Dark Univ. 48, 101870 (2025), arXiv:2410.08306 [astro-ph.CO]

    work page arXiv 2025

  13. [13]

    Motta, M

    V. Motta, M. A. Garc´ ıa-Aspeitia, A. Hern´ andez-Almada, J. Maga˜ na, and T. Verdugo, Universe 7, 163 (2021), arXiv:2104.04642 [astro-ph.CO]

    work page arXiv 2021

  14. [14]

    The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics

    E. Di Valentino et al., (2025), arXiv:2504.01669 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  15. [15]

    DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

    M. Abdul Karim et al. (DESI), (2025), arXiv:2503.14738 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  16. [16]

    T. K. Mukherjee, H. Chen, and M. Huang, Phys. Rev. D 82 (2010), 10.1103/physrevd.82.034015

    work page doi:10.1103/physrevd.82.034015 2010

  17. [17]

    Nishimura and M

    H. Nishimura and M. C. Ogilvie, Phys. Rev. D 81 (2010), 10.1103/physrevd.81.014018

    work page doi:10.1103/physrevd.81.014018 2010

  18. [18]

    Fukushima, Phys

    K. Fukushima, Phys. Lett. B 591, 277 (2004)

    work page 2004

  19. [19]

    Fukushima and V

    K. Fukushima and V. Skokov, Prog. Part. Nucl. Phys. 96, 154 (2017)

    work page 2017

  20. [20]

    Gattringer, Nucl

    C. Gattringer, Nucl. Phys. B 850, 242 (2011)

    work page 2011

  21. [21]

    From confinement to dark energy

    B. Holdom, Phys. Lett. B 697, 351 (2011), arXiv:1012.0551 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  22. [22]

    F. R. Urban and A. R. Zhitnitsky, Nucl. Phys. B 835, 135 (2010), arXiv:0909.2684 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  23. [23]

    Dark Energy and QCD Ghost

    N. Ohta, Phys. Lett. B 695, 41 (2011), arXiv:1010.1339 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  24. [24]

    Ratti, M

    C. Ratti, M. A. Thaler, and W. Weise, Phys. Rev. D 73, 014019 (2006)

    work page 2006

  25. [25]

    Abuki, R

    H. Abuki, R. Anglani, R. Gatto, G. Nardulli, and M. Ruggieri, Phys. Rev. D 78, 034034 (2008)

    work page 2008

  26. [26]

    Hansen, W

    H. Hansen, W. M. Alberico, A. Beraudo, A. Molinari, M. Nardi, and C. Ratti, Phys. Rev. D 75, 065004 (2007)

    work page 2007

  27. [27]

    S. K. Ghosh, P. K. Mohan, H. Mishra, and V. K. Singh, Phys. Rev. D 73, 114007 (2006)

    work page 2006

  28. [28]

    Fukushima, Phys

    K. Fukushima, Phys. Rev. D 77, 114028 (2008)

    work page 2008

  29. [29]

    F. R. Urban and A. R. Zhitnitsky, Physical Review D 83, 123532 (2011)

    work page 2011

  30. [30]

    Ohta, Physics Letters B 695, 41 (2011)

    N. Ohta, Physics Letters B 695, 41 (2011)

    work page 2011

  31. [31]

    Foreman-Mackey, D

    D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Good- man, Publications of the Astronomical Society of the Pa- cific 125, 306 (2013)

    work page 2013

  32. [32]

    Moresco, A

    M. Moresco, A. Cimatti, R. Jimenez, and et. al., Journal of Cosmology and Astroparticle Physics 2012, 006006 (2012)

    work page 2012

  33. [33]

    Moresco, Monthly Notices of the Royal Astronomical Society: Letters 450, L16L20 (2015)

    M. Moresco, Monthly Notices of the Royal Astronomical Society: Letters 450, L16L20 (2015)

    work page 2015

  34. [34]

    Moresco, L

    M. Moresco, L. Pozzetti, A. Cimatti, R. Jimenez, C. Maraston, L. Verde, D. Thomas, A. Citro, R. Tojeiro, and D. Wilkinson, Journal of Cosmology and Astropar- ticle Physics 2016, 014014 (2016)

    work page 2016

  35. [35]

    Moresco, R

    M. Moresco, R. Jimenez, L. Verde, A. Cimatti, and L. Pozzetti, The Astrophysical Journal 898, 82 (2020)

    work page 2020

  36. [36]

    K. Jiao, N. Borghi, M. Moresco, and T.-J. Zhang, ApJS 265, 48 (2023)

    work page 2023

  37. [37]

    Tomasetti, M

    E. Tomasetti, M. Moresco, N. Borghi, K. Jiao, A. Cimatti, L. Pozzetti, A. C. Carnall, R. J. McLure, and L. Pentericci, A&A 679, A96 (2023)

    work page 2023

  38. [38]

    D. M. Scolnic, D. O. Jones, A. Rest, and et. al., Astro- phys. J. 859, 101 (2018)

    work page 2018

  39. [39]

    Brout, D

    D. Brout, D. Scolnic, B. Popovic, and et. al., The As- trophysical Journal 938, 110 (2022)

    work page 2022

  40. [40]

    Conley, J

    A. Conley, J. Guy, M. Sullivan, and et. al., The Astro- physical Journal Supplement Series 192, 1 (2010)

    work page 2010

  41. [41]

    A. L. Gonz´ alez-Mor´ an, R. Ch´ avez, R. Terlevich, E. Ter- levich, F. Bresolin, D. Fern´ andez-Arenas, M. Plionis, S. Basilakos, J. Melnick, and E. Telles, Monthly No- tices of the Royal Astronomical Society487, 4669 (2019), arXiv:1906.02195 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  42. [42]

    A. L. Gonz´ alez-Mor´ an, R. Ch´ avez, E. Terlevich, R. Ter- levich, D. Fern´ andez-Arenas, F. Bresolin, M. Plionis, J. Melnick, S. Basilakos, and E. Telles, MNRAS 505, 1441 (2021), arXiv:2105.04025 [astro-ph.CO]

    work page arXiv 2021

  43. [43]

    Cao, Shuo, Zheng, Xiaogang, Biesiada, Marek, Qi, Jingzhao, Chen, Yun, and Zhu, Zong-Hong, A&A 606, A15 (2017)

    work page 2017

  44. [44]

    Akaike, IEEE Transactions on Automatic Control 19, 716 (1974)

    H. Akaike, IEEE Transactions on Automatic Control 19, 716 (1974)

    work page 1974

  45. [45]

    Sugiura, Communications in Statistics - Theory and Methods 7, 13 (1978)

    N. Sugiura, Communications in Statistics - Theory and Methods 7, 13 (1978)

    work page 1978

  46. [46]

    Schwarz, Ann

    G. Schwarz, Ann. Statist. 6, 461 (1978)

    work page 1978

  47. [47]

    Saucedo, A

    J. Saucedo, A. Paz, F. Flores-Baez, and J. Ibarra, Open Physics 21, 20230133 (2023)

    work page 2023

  48. [48]

    S. M. Carroll, Living Rev. Rel. 4, 1 (2001), arXiv:astro- ph/0004075 [astro-ph]

    work page arXiv 2001

  49. [49]

    Dynamical dark energy in light of the latest observations

    G.-B. Zhao et al. , Nature Astron. 1, 627 (2017), arXiv:1701.08165 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  50. [50]

    Di Valentino et al

    E. Di Valentino et al. , Astropart. Phys. 131, 102605 (2021), arXiv:2008.11284 [astro-ph.CO]

    work page arXiv 2021

  51. [51]

    2016 [arXiv:1606.00180]

    L. Amendola et al. , Living Rev. Rel. 21, 2 (2018), arXiv:1606.00180 [astro-ph.CO]

    work page arXiv 2018

  52. [52]

    Blum et al

    B. Blum et al. , in Snowmass 2021 (2022) arXiv:2203.07220 [astro-ph.CO]

    work page arXiv 2021