Recognition: 2 theorem links
· Lean TheoremRevisiting the Matter Creation Process: Observational Constraints on Gravitationally Induced Dark Energy and the Hubble Tension
Pith reviewed 2026-05-16 12:11 UTC · model grok-4.3
The pith
Gravitationally induced particle creation fits data like ΛCDM while cutting the Hubble tension to 2.4-3 sigma.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Within the thermodynamic description of open systems, gravitationally induced particle creation with four late-time (0<z<3) phenomenological rate parametrizations yields constraints on the extra component's equation-of-state parameter that are consistent with dark energy, while disfavoring creation of pressureless matter; the resulting models match ΛCDM fits and reduce the Hubble tension from 4.3 sigma to 2.4-3 sigma when early and late datasets are treated separately.
What carries the argument
Four phenomenological parametrizations of the gravitationally induced particle creation rate, with free equation-of-state w_E for the created component, applied only at late times in an open thermodynamic system.
If this is right
- Particle creation of pressureless matter is ruled out by the data.
- One parametrization produces effective dynamical dark-energy evolution.
- All models achieve statistical fits comparable to ΛCDM.
- Separate early- and late-time analyses lower the Hubble tension to 2.4-3 sigma.
Where Pith is reading between the lines
- Future high-redshift Hubble measurements could test whether the late-time restriction remains valid.
- The approach may supply a physical mechanism underlying other phenomenological dark-energy parametrizations.
- Allowing creation at earlier epochs could be checked against big-bang nucleosynthesis bounds to see if it introduces new tensions.
- The framework offers a route to connect thermodynamic non-equilibrium processes with observed cosmic acceleration.
Load-bearing premise
Deviations from ΛCDM due to particle creation are confined to the redshift range 0 to 3 and are accurately captured by the four chosen parametrizations of the creation rate.
What would settle it
A joint analysis of the full dataset that still finds the Hubble tension above 4 sigma, or direct evidence of significant particle creation at redshifts greater than 3.
Figures
read the original abstract
The Hubble tension and the unknown origin of dark energy motivate the exploration of alternative mechanisms for late-time cosmic acceleration. We investigate gravitationally induced particle creation (PC) as a non-equilibrium process that can effectively mimic dynamical dark energy. Within the thermodynamic framework of open systems, we adopt an agnostic approach to the extra created component, leaving its equation-of-state parameter $w_E$ free. We consider four phenomenological parametrisations of the PC rate, allowing deviations from the standard cosmological model ($\Lambda$CDM) only at late times ($0<z<3$). The PC models are constrained using a joint analysis of cosmic chronometers, Type Ia supernovae, local $H_0$ measurements, baryon acoustic oscillations, and cosmic microwave background data. The constraints on $w_E$ are consistent with dark energy, while particle creation of pressureless matter is disfavoured. All PC scenarios provide fits comparable to $\Lambda$CDM, with one showing effective dynamical dark-energy behaviour. When early- and late-time datasets are analysed separately, the PC models reduce the Hubble tension to $\simeq 2.4\,\sigma$--$3\,\sigma$, compared to $4.3\,\sigma$ in $\Lambda$CDM. Gravitationally induced dark energy thus offers a consistent late-time extension of $\Lambda$CDM and a viable theoretical framework for dynamical dark energy.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript investigates gravitationally induced particle creation (PC) within an open thermodynamic system framework as a mechanism to generate effective dynamical dark energy. It adopts four phenomenological parametrizations of the PC rate, restricted to late times (0 < z < 3), leaves the equation-of-state parameter w_E free, and constrains the models using cosmic chronometers, Type Ia supernovae, local H0, BAO, and CMB data. The key claims are that the PC models provide fits comparable to ΛCDM, with constraints on w_E consistent with dark energy, and that splitting early- and late-time datasets reduces the Hubble tension from 4.3σ in ΛCDM to 2.4σ–3σ in the PC scenarios.
Significance. If the central results hold, this work offers a thermodynamically motivated alternative to standard dark energy that can alleviate the Hubble tension at late times without additional fields. The approach of treating the created component agnostically with free w_E and comparing to data provides a testable framework, though its robustness depends on the validity of the imposed restrictions.
major comments (3)
- [§3] §3 (Phenomenological parametrizations): The four specific forms chosen for the particle creation rate are introduced directly as phenomenological functions without derivation from the open-system thermodynamic equations; because the reported tension reduction to 2.4–3σ is obtained only under these forms plus the explicit 0<z<3 cutoff, it remains unclear whether the improvement follows from the framework or is enabled by the parametrization choice.
- [Results section] Results section (tension quantification): The Hubble tension reduction is demonstrated exclusively for the split early-time versus late-time datasets under the late-time-only restriction; no analysis is shown for the full combined dataset or with the cutoff removed, leaving the robustness of the central claim untested.
- [§4] §4 (Constraints and likelihood): The statements that w_E is consistent with dark energy and pressureless-matter creation is disfavoured rest on joint fits, yet the manuscript provides neither the explicit likelihood forms, full posterior tables, nor error-budget breakdown; this gap prevents independent verification that the statistical conclusions are fully supported by the data.
minor comments (3)
- [§2] Notation for w_E should be introduced with an explicit equation relating it to the created component's energy density and pressure to avoid confusion with standard dark-energy parametrizations.
- [Figures] Figure captions comparing PC models to ΛCDM would be clearer if they included the numerical Δχ² or evidence ratios for each scenario.
- [§2] A brief statement on the thermodynamic consistency of setting particle creation to zero for z>3 would help readers assess the physical motivation of the cutoff.
Simulated Author's Rebuttal
We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below, providing clarifications where needed and indicating planned revisions to improve the paper.
read point-by-point responses
-
Referee: [§3] §3 (Phenomenological parametrizations): The four specific forms chosen for the particle creation rate are introduced directly as phenomenological functions without derivation from the open-system thermodynamic equations; because the reported tension reduction to 2.4–3σ is obtained only under these forms plus the explicit 0<z<3 cutoff, it remains unclear whether the improvement follows from the framework or is enabled by the parametrization choice.
Authors: We acknowledge that the four forms are introduced phenomenologically, as explicitly stated in the manuscript. However, they are chosen to represent plausible late-time behaviors consistent with the open thermodynamic system framework derived in Sec. 2, where the particle creation rate Γ enters the effective energy density and pressure. These specific parametrizations follow common choices in the literature for Γ(z) that allow dynamical effects confined to low redshifts. The tension reduction arises from the framework's provision of an effective dynamical dark energy component (with free w_E) at late times, rather than from arbitrary parametrization alone. To strengthen the connection, we will revise §3 to include a more explicit derivation linking the forms to the thermodynamic equations and discuss their generality within the model class. revision: partial
-
Referee: [Results section] Results section (tension quantification): The Hubble tension reduction is demonstrated exclusively for the split early-time versus late-time datasets under the late-time-only restriction; no analysis is shown for the full combined dataset or with the cutoff removed, leaving the robustness of the central claim untested.
Authors: The Hubble tension is conventionally quantified via separate early-time (primarily CMB) and late-time (CC, SNIa, BAO, local H0) constraints, as this isolates the discrepancy the PC models target. Because the models are constructed as late-time extensions (0<z<3), the split analysis directly demonstrates their impact. We agree that results for the full combined dataset and a test with the cutoff relaxed would further test robustness. We will add these analyses to the revised Results section, including constraints from the joint dataset and a brief exploration of a wider redshift range. revision: yes
-
Referee: [§4] §4 (Constraints and likelihood): The statements that w_E is consistent with dark energy and pressureless-matter creation is disfavoured rest on joint fits, yet the manuscript provides neither the explicit likelihood forms, full posterior tables, nor error-budget breakdown; this gap prevents independent verification that the statistical conclusions are fully supported by the data.
Authors: We agree that additional statistical details would improve transparency and verifiability. In the revised manuscript we will add an appendix containing the explicit likelihood functions for each dataset, full posterior tables for the key parameters (including w_E and the PC rate coefficients), and an error-budget breakdown that supports the statements on consistency with dark energy and the disfavoring of pressureless matter creation. revision: yes
Circularity Check
No significant circularity detected
full rationale
The paper explicitly adopts four phenomenological parametrizations of the creation rate with a late-time cutoff (0<z<3) and leaves w_E free, then performs standard joint and split-dataset fits to observational data. No claimed first-principles derivation or prediction reduces by construction to the fitted parameters or to a self-citation; the tension reduction (2.4-3σ vs 4.3σ) is reported as the direct numerical outcome of those fits. The thermodynamic open-system framework supplies only the general motivation, not the specific functional forms or cutoff, which are stated as chosen. The analysis is therefore a conventional data-driven model comparison with no load-bearing self-referential step.
Axiom & Free-Parameter Ledger
free parameters (2)
- w_E
- PC-rate parameters
axioms (2)
- domain assumption Universe treated as an open thermodynamic system in which gravity induces particle creation
- ad hoc to paper Deviations from ΛCDM occur only at late times (0 < z < 3)
Lean theorems connected to this paper
-
IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
We consider four phenomenological parametrisations of the PC rate, allowing deviations from the standard cosmological model (ΛCDM) only at late times (0<z<3).
-
IndisputableMonolith/Foundation/RealityFromDistinction.leanreality_from_one_distinction unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
The PC models are constrained using a joint analysis... yielding H0 ≃69.3 km s⁻¹ Mpc⁻¹
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Forward citations
Cited by 2 Pith papers
-
Evidence for deviation in gravitational light deflection from general relativity at cosmological scales with KiDS-Legacy and CMB lensing
KiDS-Legacy weak lensing plus CMB data yields a 3 sigma deviation in light deflection from GR in a Lambda CDM background, with the signal driven by large-scale CMB lensing amplitudes.
-
Measuring neutrino mass in light of ACT DR6 and DESI DR2
New ACT and DESI data yield model-dependent upper limits on sum of neutrino masses, with holographic dark energy giving the tightest bounds and a consistent preference for degenerate hierarchy.
Reference graph
Works this paper leans on
-
[1]
C. L. Bennettet al.(WMAP), Astrophys. J. Suppl.208, 20 (2013), arXiv:1212.5225 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2013
-
[2]
Planck 2018 results. VI. Cosmological parameters
N. Aghanimet al.(Planck), Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2020
-
[3]
N. Aghanimet al.(Planck), Astron. Astrophys.641, A1 (2020), arXiv:1807.06205 [astro-ph.CO]
-
[4]
S. Aiolaet al.(ACT), JCAP12, 047, arXiv:2007.07288 [astro-ph.CO]
-
[5]
The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and $\Lambda$CDM Parameters
T. Louiset al.(Atacama Cosmology Telescope), JCAP 11, 062, arXiv:2503.14452 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv
-
[6]
E. Camphuiset al.(SPT-3G), SPT-3G D1: CMB tem- perature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G Main field (2025), arXiv:2506.20707 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2019
-
[7]
The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the Local Hubble Constant
F. Beutler, C. Blake, M. Colless, D. H. Jones, L. Staveley-Smith, L. Campbell, Q. Parker, W. Saun- ders, and F. Watson, Mon. Not. Roy. Astron. Soc.416, 17 FIG. 7. Left panel: plot of the function H(z) 1+z in the PC1 model for different values ofα. The parameterw E was fixed to the value−0.9. The trivial casew E =−1 is not interesting, since it ends up wit...
work page internal anchor Pith review Pith/arXiv arXiv 2011
-
[8]
A. J. Ross, L. Samushia, C. Howlett, W. J. Percival, A. Burden, and M. Manera, Mon. Not. Roy. Astron. Soc.449, 835 (2015), arXiv:1409.3242 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2015
-
[9]
S. Alamet al.(BOSS), Mon. Not. Roy. Astron. Soc. 470, 2617 (2017), arXiv:1607.03155 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2017
-
[10]
S. Alamet al.(eBOSS), Phys. Rev. D103, 083533 (2021), arXiv:2007.08991 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2021
- [11]
-
[12]
DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints
M. Abdul Karimet al.(DESI), Phys. Rev. D112, 083515 (2025), arXiv:2503.14738 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2025
-
[13]
G. Guet al.(DESI), Dynamical Dark Energy in light of the DESI DR2 Baryonic Acoustic Oscillations Mea- surements (2025), arXiv:2504.06118 [astro-ph.CO]
- [14]
-
[15]
The Pantheon+ Analysis: Cosmological Constraints
D. Broutet al., Astrophys. J.938, 110 (2022), arXiv:2202.04077 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2022
-
[16]
The Pantheon+ Analysis: The Full Dataset and Light-Curve Release
D. Scolnicet al., Astrophys. J.938, 113 (2022), arXiv:2112.03863 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2022
-
[17]
T. M. C. Abbottet al.(DES), Astrophys. J. Lett.973, L14 (2024), arXiv:2401.02929 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2024
-
[18]
M. Moresco, L. Pozzetti, A. Cimatti, R. Jimenez, C. Maraston, L. Verde, D. Thomas, A. Citro, R. Tojeiro, and D. Wilkinson, JCAP05, 014, arXiv:1601.01701 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv
-
[19]
M. Moresco, Addressing the Hubble tension with cosmic chronometers (2023), arXiv:2307.09501 [astro-ph.CO]
- [20]
-
[21]
I. Prigogine, J. Geheniau, E. Gunzig, and P. Nardone, Gen. Rel. Grav.21, 767 (1989)
work page 1989
-
[22]
M. O. Calvao, J. A. S. Lima, and I. Waga, Phys. Lett. A162, 223 (1992)
work page 1992
-
[23]
M. P. Freaza, R. S. de Souza, and I. Waga, Phys. Rev. D66, 103502 (2002)
work page 2002
-
[24]
S. Pan, J. de Haro, A. Paliathanasis, and R. J. Slagter, Mon. Not. Roy. Astron. Soc.460, 1445 (2016), arXiv:1601.03955 [gr-qc]
work page internal anchor Pith review Pith/arXiv arXiv 2016
- [25]
-
[26]
E. Elizalde, M. Khurshudyan, and S. D. Odintsov, Eur. Phys. J. C84, 782 (2024), arXiv:2407.20285 [gr-qc]
-
[27]
Quintessence, Cosmic Coincidence, and the Cosmological Constant
I. Zlatev, L.-M. Wang, and P. J. Steinhardt, Phys. Rev. Lett.82, 896 (1999), arXiv:astro-ph/9807002
work page internal anchor Pith review Pith/arXiv arXiv 1999
- [28]
- [29]
- [30]
-
[31]
H. Gohar and V. Salzano, Eur. Phys. J. C81, 338 (2021), arXiv:2008.09635 [gr-qc]
- [32]
- [33]
-
[34]
O. Akarsu and N. M. Uzun, Phys. Dark Univ.40, 101194 (2023), arXiv:2301.11204 [gr-qc]
- [35]
- [36]
-
[37]
G. Montani, N. Carlevaro, and M. De Angelis, Entropy 26, 662 (2024), arXiv:2407.12409 [gr-qc]
-
[38]
M. Marciu, Eur. Phys. J. C84, 1191 (2024), [Erratum: Eur.Phys.J.C 84, 1285 (2024)], arXiv:2410.04584 [gr-qc]
-
[39]
S. Ganjizadeh, A. Amani, and M. A. Ramzanpour, Chin. Phys. C46, 125104 (2022), arXiv:2208.07710 [gr- qc]
- [40]
-
[41]
V. H. C´ ardenas, M. Cruz, and S. Lepe, Eur. Phys. J. Plus139, 642 (2024), arXiv:2302.10155 [gr-qc]. 18 FIG. 8. Plots of the function H(z) 1+z in the PC1 model for different values ofβ. The parameterw E was fixed to the value−0.9 and−1.1 on the left and right panels, respectively. The trivial casew E =−1 is not interesting, since it ends up with the ΛCDM ...
- [42]
- [43]
- [44]
-
[45]
Tensions between the Early and the Late Universe
L. Verde, T. Treu, and A. G. Riess, Nature Astron.3, 891 (2019), arXiv:1907.10625 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2019
-
[46]
S. Vagnozzi, Phys. Rev. D102, 023518 (2020), arXiv:1907.07569 [astro-ph.CO]
-
[47]
E. Di Valentinoet al., Astropart. Phys.131, 102605 (2021), arXiv:2008.11284 [astro-ph.CO]
-
[48]
In the Realm of the Hubble tension $-$ a Review of Solutions
E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri, D. F. Mota, A. G. Riess, and J. Silk, Class. Quant. Grav.38, 153001 (2021), arXiv:2103.01183 [astro-ph.CO]. 19 FIG. 9. Plot of the effective equation of state parameter of dark energyw eff DE(z) in the PC1 model for different values ofα. The extra parameters are setw E =−0.9 andβ= 1, ...
work page internal anchor Pith review Pith/arXiv arXiv 2021
-
[49]
L. Perivolaropoulos and F. Skara, New Astron. Rev.95, 101659 (2022), arXiv:2105.05208 [astro-ph.CO]
-
[50]
N. Sch¨ oneberg, G. Franco Abell´ an, A. P´ erez S´ anchez, S. J. Witte, V. Poulin, and J. Lesgourgues, Phys. Rept. 984, 1 (2022), arXiv:2107.10291 [astro-ph.CO]
- [51]
-
[52]
E. Abdallaet al., JHEAp34, 49 (2022), arXiv:2203.06142 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2022
- [53]
-
[54]
M. Kamionkowski and A. G. Riess, Ann. Rev. Nucl. Part. Sci.73, 153 (2023), arXiv:2211.04492 [astro- ph.CO]
-
[55]
Giar` e, CMB Anomalies and the Hubble Tension (2023), arXiv:2305.16919 [astro-ph.CO]
W. Giar` e, CMB Anomalies and the Hubble Tension (2023), arXiv:2305.16919 [astro-ph.CO]
-
[56]
J.-P. Hu and F.-Y. Wang, Universe9, 94 (2023), arXiv:2302.05709 [astro-ph.CO]
- [57]
-
[58]
E. Di Valentino and D. Brout, eds.,The Hubble Con- stant Tension, Springer Series in Astrophysics and Cos- mology (Springer, 2024)
work page 2024
-
[59]
L. Perivolaropoulos, Phys. Rev. D110, 123518 (2024), arXiv:2408.11031 [astro-ph.CO]
-
[60]
E. Di Valentinoet al.(CosmoVerse Network), Phys. Dark Univ.49, 101965 (2025), arXiv:2504.01669 [astro- ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2025
-
[61]
A. G. Riesset al., Astrophys. J. Lett.934, L7 (2022), arXiv:2112.04510 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2022
-
[62]
S. Casertanoet al.(H0DN), The Local Distance Net- work: a community consensus report on the measure- ment of the Hubble constant at 1% precision (2025), arXiv:2510.23823 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2025
- [63]
-
[64]
T. Schiavone, G. Montani, M. G. Dainotti, B. De Si- mone, E. Rinaldi, and G. Lambiase, in17th Italian- Korean Symposium on Relativistic Astrophysics(2022) arXiv:2205.07033 [astro-ph.CO]
-
[65]
T. Schiavone, G. Montani, and F. Bombacigno, Mon. Not. Roy. Astron. Soc.522, L72 (2023), arXiv:2211.16737 [gr-qc]
- [66]
-
[67]
G. Montani, M. De Angelis, F. Bombacigno, and N. Car- levaro, Mon. Not. Roy. Astron. Soc.527, L156 (2023), arXiv:2306.11101 [gr-qc]
- [68]
-
[69]
T. Schiavone and G. Montani, Nuovo Cim. C48, 105 (2025), arXiv:2408.01410 [gr-qc]
- [70]
-
[71]
G. Montani, M. De Angelis, and M. G. Dainotti, Phys. Dark Univ.49, 101969 (2025), arXiv:2506.13288 [astro- ph.CO]
-
[72]
D. Efstratiou, E. A. Paraskevas, and L. Perivolaropou- los, e-print (2025), arXiv:2511.04610 [astro-ph.CO]
-
[73]
S. D’Onofrio, S. Odintsov, and T. Schiavone, e-print (2025), arXiv:2511.06924 [gr-qc]
-
[74]
On the Metric $f(R)$ gravity Viability in Accounting for the Binned Supernovae Data
A. Valletta, G. Montani, M. G. Dainotti, and E. Fazzari, e-print (2025), arXiv:2512.19568 [gr-qc]
work page internal anchor Pith review Pith/arXiv arXiv 2025
-
[75]
G. Montani, L. A. Escamilla, N. Carlevaro, and E. Di Valentino, Phys. Rev. D113, 023507 (2026), arXiv:2512.20193 [astro-ph.CO]
-
[76]
G. Montani, N. Carlevaro, and M. G. Dainotti, Phys. Dark Univ.44, 101486 (2024), arXiv:2311.04822 [gr-qc]
-
[77]
G. Montani, N. Carlevaro, and M. G. Dainotti, Phys. Dark Univ.48, 101847 (2025), arXiv:2411.07060 [gr-qc]
- [78]
-
[79]
Probing the interaction between dark matter and dark energy in the presence of massive neutrinos
S. Kumar and R. C. Nunes, Phys. Rev. D94, 123511 (2016), arXiv:1608.02454 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv 2016
-
[80]
Constraints on the Coupling between Dark Energy and Dark Matter from CMB data
R. Murgia, S. Gariazzo, and N. Fornengo, JCAP04, 014, arXiv:1602.01765 [astro-ph.CO]
work page internal anchor Pith review Pith/arXiv arXiv
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.