REVIEW
Testing cosmic acceleration from thermogravity without vacuum energy
Cosmology and Nongalactic Astrophysics · Submitted 24 Sep 2026 · 53 references
Pith's verdict: First background-level test of thermogravity: honest, internally consistent, citable, but the 2.2σ ξCDM preference is anchor-fragile and partly a free-H0 shape effect.
T0 · AI review
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Referee report
The paper
The paper claims
This paper presents a first background-level test of a thermogravity theory whose trace-free Einstein equations leave the cosmological constant gravitationally inert, asking whether late-time acceleration can instead be produced by…
The reading
What carries the argument
The load-bearing objects are the trace-free field equations $R_{\mu\nu} - \tfrac{1}{4}Rg_{\mu\nu} = 8\pi G(T_{\mu\nu} - \tfrac{1}{4}Tg_{\mu\nu})$ together with a projected non-conservation law, $-n^\mu\nabla^\nu T_{\mu\nu} = (1/L_2)(n^\mu n^\nu + \tfrac{1}{3}h^{\mu\nu})T_{\mu\nu}$, tied to a preferred thermodynamic frame $n^\mu$. The parameter $L_2$, or its dimensionless version $\xi_c = 1/(H_0 L_2)$, sets the timescale on which the thermodynamic cycle departs from its degenerate heat-only limit, with $\xi_c \to 0$ recovering ΛCDM. For the CDM-only model the decisive ingredient is the effective present-day CDM density $\omega_c^{\mathrm{eff}} = \rho_c e^{-t_0/L_2}$, which reproduces the early-time CDM density when evolved as $a^{-3}$, allowing the standard $z_{\mathrm{drag}}$ fitting formula and the compressed CMB likelihood to be applied unchanged.
Extended reading notes
Core claim
The central claim is that cosmic acceleration can arise from energy non-conservation in a trace-free gravitational theory without a gravitating vacuum energy, but only if the violation is confined to the dark matter sector. The universal model is intrinsically rigid: raising the matter density improves the intermediate-redshift normalization of H(z) preferred by BAO, yet also raises q0 = −1 + 3Ωm/2 and weakens the present acceleration, so the two-probe fit fails badly (Δχ² ≃ 51, lnB ≃ −26 against ΛCDM). Restricting non-conservation to CDM keeps baryonic, photon, and neutrino observables standard at background level, permitting a self-contained analysis in which the one-parameter ξCDM model beats ΛCDM by Δχ² = −4.85 with lnB = 2.77 for the supernova-plus-DESI-BAO combination. The paper also reports that ξCDM does not resolve the Hubble tension: with BBN or CMB anchors the sound horizon grows and H0 falls, worsening the discrepancy with the distance ladder.
Load-bearing premise
For the positive ξCDM result, everything rests on the claim that the sound-horizon calibration survives in this model: the effective CDM density ω_eff^c defined by Eq. (25) must correctly reproduce the early-time CDM density when evolved as a⁻³, so that the z_drag fitting formula and the compressed CMB likelihood, both built on ΛCDM-style early-time species evolution, remain valid.
Editorial extensions
If this is right
- If ξCDM is correct, late-time acceleration can be produced by dark-sector energy creation with no gravitating vacuum energy, at the price of a single extra parameter over flat ΛCDM.
- Under the standard observational dictionary, the universal thermogravity model is effectively excluded by DESI BAO at high significance (Δχ² ≃ 51).
- ξCDM provides a better fit to background data than wCDM, with a preference comparable to the two-parameter w0waCDM, making it a concrete rival expansion model for supernova and BAO combinations.
- Because ξCDM pushes H0 lower when calibrated with early-Universe anchors, it cannot be invoked to soften the Hubble tension; its case must rest on the shape of the expansion history rather than on the absolute distance scale.
Reading between the lines
- As an editorial extension, the ξCDM signal is compatible with what one would expect if the true expansion history carried slightly less matter at intermediate redshifts than ΛCDM predicts; it is worth testing whether a milder, parameter-light modification of the effective matter density absorbs the same Δχ² improvement without invoking thermogravity.
- Since the preferred frame is physical, perturbation-level predictions such as CMB anisotropies and the growth rate cannot be imported from ΛCDM, so a dedicated perturbative treatment would either confirm the roughly 2σ background preference or expose it as a calibration artifact.
- The universal model's exclusion is conditional on the standard observational dictionary staying intact; in a genuinely universal theory, redshifts, distances, and rulers might all be reinterpreted, which is exactly why the authors treat the exclusion as formal rather than complete.
Original abstract
We present a first background-level observational test of a thermogravity theory in which the Einstein equations are clipped to a trace-free version, the cosmological constant $\Lambda$ does not gravitate, and controlled violations of energy conservation obstruct the usual reinstatement of $\Lambda$ as an integration constant. We therefore set $\Lambda=0$ and ask whether late-time acceleration can instead be generated solely by energy non-conservation, with no extra background parameter relative to flat $\Lambda\mathrm{CDM}$. We contrast a minimal universal implementation with a model in which only CDM partakes in non-conservation. The universal model is strongly disfavored when combining Supernovae and BAO distances, with the inclusion of DESI BAO worsening the fit by $\Delta\chi^2\simeq 51$ relative to $\Lambda\mathrm{CDM}$, because matter creation ties the intermediate-redshift normalization of $H(z)$ too rigidly to the present acceleration. This conclusion, however, should be interpreted with caution, since universal non-conservation would modify the observational dictionary itself. By contrast, restricting non-conservation to CDM leaves baryonic and photon observables unaffected at the background level and therefore allows a self-contained analysis. The resulting $\xi\mathrm{CDM}$ model, which can be thought of as a one parameter extension of $\Lambda\mathrm{CDM}$, provides an improved fit relative to $\Lambda\mathrm{CDM}$ for the background dataset combinations considered, with improvements reaching $\Delta\chi^2=-4.85$ and a maximum Bayesian preference of $\ln\mathcal{B}=2.77$. However, when the BAO ruler is calibrated using BBN or CMB information, the reduced effective early-time CDM density increases the sound horizon and drives $H_0$ towards lower values, thereby increasing rather than alleviating the tension with the distance-ladder calibration.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We present a first background-level observational test of a thermogravity theory in which the Einstein equations are clipped to a trace-free version, the cosmological constant $\Lambda$ does not gravitate, and controlled violations of energy conservation obstruct the usual reinstatement of $\Lambda$ as an integration constant. We therefore set $\Lambda=0$ and ask whether late-time acceleration can instead be generated solely by energy non-conservation, with no extra background parameter relative to flat $\Lambda\mathrm{CDM}$. We contrast a minimal universal implementation with a model in which only CDM partakes in non-conservation. The universal model is strongly disfavored when combining Supernovae and BAO distances, with the inclusion of DESI BAO worsening the fit by $\Delta\chi^2\simeq 51$ relative to $\Lambda\mathrm{CDM}$, because matter creation ties the intermediate-redshift normalization of $H(z)$ too rigidly to the present acceleration. This conclusion, however, should be interpreted with caution, since universal non-conservation would modify the observational dictionary itself. By contrast, restricting non-conservation to CDM leaves baryonic and photon observables unaffected at the background level and therefore allows a self-contained analysis. The resulting $\xi\mathrm{CDM}$ model, which can be thought of as a one parameter extension of $\Lambda\mathrm{CDM}$, provides an improved fit relative to $\Lambda\mathrm{CDM}$ for the background dataset combinations considered, with improvements reaching $\Delta\chi^2=-4.85$ and a maximum Bayesian preference of $\ln\mathcal{B}=2.77$. However, when the BAO ruler is calibrated using BBN or CMB information, the reduced effective early-time CDM density increases the sound horizon and drives $H_0$ towards lower values, thereby increasing rather than alleviating the tension with the distance-ladder calibration.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a first background-level observational test of a thermogravity theory in which the Einstein equations are clipped to a trace-free version, the cosmological constant $\Lambda$ does not gravitate, and controlled violations of energy conservation obstruct the usual reinstatement of $\Lambda$ as an integration constant. | contribution 0.91 | 0.71 | 0.06 | asserted 0.98 |
| s1 | We therefore set $\Lambda=0$ and ask whether late-time acceleration can instead be generated solely by energy non-conservation, with no extra background parameter relative to flat $\Lambda\mathrm{CDM}$. | contribution 0.65 | 0.78 | 0.05 | asserted 0.34 |
| s2 | We contrast a minimal universal implementation with a model in which only CDM partakes in non-conservation. | method 0.75 | 0.71 | 0.03 | asserted 0.77 |
| s3 | The universal model is strongly disfavored when combining Supernovae and BAO distances, with the inclusion of DESI BAO worsening the fit by $\Delta\chi^2\simeq 51$ relative to $\Lambda\mathrm{CDM}$, because matter creation ties the intermediate-redshift normalization of $H(z)$ too rigidly to the present acceleration. | result 1.00 | 0.93 | 0.22 | asserted 1.00 |
| s4 | This conclusion, however, should be interpreted with caution, since universal non-conservation would modify the observational dictionary itself. | limitation 0.95 | 0.22 | 0.05 | hedged possibility 0.59 |
| s5 | By contrast, restricting non-conservation to CDM leaves baryonic and photon observables unaffected at the background level and therefore allows a self-contained analysis. | method 0.84 | 0.41 | 0.06 | asserted 1.00 |
| s6 | The resulting $\xi\mathrm{CDM}$ model, which can be thought of as a one parameter extension of $\Lambda\mathrm{CDM}$, provides an improved fit relative to $\Lambda\mathrm{CDM}$ for the background dataset combinations considered, with improvements reaching $\Delta\chi^2=-4.85$ and a maximum Bayesian preference of $\ln\mathcal{B}=2.77$. | result 1.00 | 0.94 | 0.42 | asserted 1.00 |
| s7 | However, when the BAO ruler is calibrated using BBN or CMB information, the reduced effective early-time CDM density increases the sound horizon and drives $H_0$ towards lower values, thereby increasing rather than alleviating the tension with the distance-ladder calibration. | limitation 0.46 | 0.79 | 0.16 | asserted 0.99 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
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Figures
Figures reproduced from arXiv:2609.29206 by the authors.
References
Discussion
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