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Logarithmic f(Q) gravity models produce intermediate Hubble constant values between Planck and SH0ES measurements.

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Logarithmic and nonlinear f(Q) models are constrained via Bayesian MCMC with cosmic chronometers, supernova, and BAO data and remain competitive with ΛCDM, with the logarithmic model yielding intermediate H0 values and lower AIC/BIC penalties.

T0 review reviewed 2026-06-26 challenge →

load-bearing objection The log f(Q) model shifts H0 to intermediate values with lower AIC/BIC than the nonlinear one, but this is a standard MCMC exercise on an existing framework. the 2 major comments →

arxiv 2606.22262 v1 pith:G6ZYVVOZ submitted 2026-06-20 gr-qc

Non-Metricity Corrections Approach to Alleviate $H _0$ Tension: The Logarithmic and Nonlinear $f(Q)$ Models

Rahul Bhagat , Kesava Chodavarapu , B. Mishra This is my paper
classification gr-qc
keywords H0 tensionf(Q) gravitysymmetric teleparallel gravitymodified gravityHubble constantcosmological constraintsBayesian analysis
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper tests whether non-metricity corrections in symmetric teleparallel gravity can help resolve the Hubble constant tension. Two f(Q) models are considered: a logarithmic one and a nonlinear saturation one. Both are constrained using cosmic chronometers, supernova data from Pantheon and DES, and BAO from SDSS and DESI. The logarithmic model stands out for giving H0 values in the middle ground and scoring better on model selection criteria than the standard model.

Core claim

Within the symmetric teleparallel framework, the logarithmic f(Q) model infers intermediate values of the Hubble constant between the Planck and SH0ES benchmarks for all combinations of cosmic chronometers, Type Ia supernovae, and BAO data, while both models remain statistically competitive with Lambda CDM and the logarithmic variant shows lower AIC and BIC values.

What carries the argument

The logarithmic and nonlinear functional forms of f(Q) in symmetric teleparallel gravity, which introduce geometric corrections to the standard expansion history without a cosmological constant.

Load-bearing premise

The chosen functional forms of f(Q) can be directly constrained by the selected observational datasets without introducing unaccounted systematic biases or inconsistencies in the underlying symmetric teleparallel framework.

What would settle it

A high-precision Hubble constant measurement from future surveys that falls clearly outside the intermediate range predicted by the logarithmic model, or new data where the model fits worse than Lambda CDM according to AIC and BIC, would challenge the central claim.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates two f(Q) gravity models—a logarithmic and a nonlinear saturation model—within symmetric teleparallel gravity as a means to alleviate the H0 tension. Using Bayesian MCMC methods constrained by cosmic chronometers, Type Ia supernovae from Pantheon, Pantheon+SH0ES, and DES SN5YR, and BAO measurements from SDSS and DESI, the authors report that both models are statistically competitive with ΛCDM. The logarithmic model is highlighted for yielding H0 values intermediate between Planck and SH0ES across dataset combinations and for having lower AIC and BIC penalties.

Significance. Should the findings be substantiated by detailed derivations and robust statistical analysis, this work would contribute to the exploration of modified gravity theories as alternatives to the cosmological constant for addressing cosmological tensions. The emphasis on the logarithmic model as more promising could guide future research in non-metricity-based cosmologies. The comprehensive dataset usage is a positive aspect.

major comments (2)
  1. [Abstract] Abstract: The abstract summarizes MCMC results and model competitiveness but provides no derivation details, error analysis, or data exclusion criteria, preventing verification that the math supports the stated claim.
  2. [Abstract] Abstract: The claim that the logarithmic model infers intermediate H0 values between Planck and SH0ES is not supported by any equations; without explicit forms or modified Friedmann equations it is impossible to determine whether these values are independent predictions or direct outputs of parameters fitted to the tension data.
minor comments (1)
  1. [Abstract] Abstract: The exact functional forms of the logarithmic and nonlinear f(Q) should be stated explicitly to allow assessment of the geometric corrections to the expansion history.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. Below we address the two major comments regarding the abstract point by point.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The abstract summarizes MCMC results and model competitiveness but provides no derivation details, error analysis, or data exclusion criteria, preventing verification that the math supports the stated claim.

    Authors: Abstracts are by design concise overviews and do not contain full derivations, error budgets or dataset selection protocols; those appear in the body of the paper. The modified Friedmann equations for both f(Q) models are derived in Section II, the MCMC implementation, covariance handling and error analysis are given in Section IV, and the data compilations (cosmic chronometers, Pantheon, Pantheon+SH0ES, DES SN5YR, SDSS and DESI BAO) are described with their standard cuts in the same section. The AIC/BIC comparison is reported in the results tables. We therefore maintain that the mathematics supporting the abstract claims is fully verifiable from the manuscript. revision: no

  2. Referee: [Abstract] Abstract: The claim that the logarithmic model infers intermediate H0 values between Planck and SH0ES is not supported by any equations; without explicit forms or modified Friedmann equations it is impossible to determine whether these values are independent predictions or direct outputs of parameters fitted to the tension data.

    Authors: The reported H0 values are the posterior means and best-fit values obtained from the MCMC chains when the model parameters are constrained by the combined datasets. The underlying dynamics are set by the modified Friedmann equation that follows from varying the logarithmic f(Q) action; the explicit functional form and the resulting H(z) expression appear in Section II (Eqs. (8)–(10)). These are therefore outputs of the fit under the model’s altered expansion history rather than independent predictions. The manuscript shows that this history permits H0 values lying between the Planck and SH0ES anchors while remaining statistically competitive with ΛCDM. revision: no

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The abstract describes a standard Bayesian MCMC analysis constraining two f(Q) functional forms against cosmic chronometers, Pantheon/Pantheon+SH0ES/DES SN compilations, and BAO data, then reporting that the logarithmic model yields intermediate H0 values with lower AIC/BIC. No derivation chain, modified Friedmann equations, explicit f(Q) forms, or self-citations appear in the provided text. Without any quoted equations or load-bearing steps that reduce to fitted inputs by construction, no instances of self-definitional, fitted-input-called-prediction, or self-citation circularity can be exhibited. The reported H0 inference is the direct output of the MCMC fit to the tension-sensitive datasets, but this is the intended statistical procedure rather than a hidden circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the ledger reflects typical elements: free parameters in the f(Q) functions that are fitted to data, plus standard cosmological modeling assumptions. No invented entities are described.

free parameters (1)
  • parameters of the logarithmic and nonlinear f(Q) functions
    These parameters are constrained via MCMC analysis against the observational datasets.
axioms (1)
  • domain assumption FLRW metric applies in symmetric teleparallel gravity with the chosen f(Q) forms
    Implicit foundation for deriving the modified expansion history.

reviewed 2026-06-26 · how reviews work

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Cite this review

Pith. "Pith review of Non-Metricity Corrections Approach to Alleviate $H _0$ Tension: The Logarithmic and Nonlinear $f(Q)$ Models." pith.science (2026). https://pith.science/paper/G6ZYVVOZ

@misc{pith2026260622262,
  author       = {Pith},
  title        = {Pith review of: Non-Metricity Corrections Approach to Alleviate $H _0$ Tension: The Logarithmic and Nonlinear $f(Q)$ Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G6ZYVVOZ}},
  note         = {Machine review of arXiv:2606.22262}
}
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abstract

The persistent discrepancy between early-time and late-Universe measurements of the Hubble constant commonly known as the $H_0$ tension remains one of the most pressing open questions in modern cosmology. In this work, we explore whether modifications to the gravitational sector, specifically within the framework of symmetric teleparallel gravity, can offer a viable pathway toward alleviating this tension. We consider two functional forms of $f(Q)$ gravity: a logarithmic model and a nonlinear saturation model, both of which introduce geometric corrections to the standard expansion history without invoking a cosmological constant. Constraining these models through a Bayesian MCMC analysis against a comprehensive suite of observational data, including cosmic chronometers, Type Ia supernova compilations (Pantheon, Pantheon$+$SH0ES, and DES SN5YR), and BAO measurements from SDSS and DESI, we find that both models remain statistically competitive with $\Lambda$CDM. The logarithmic model, in particular, consistently infers intermediate values of $H_0$ between the \textit{Planck} and SH0ES benchmarks across all dataset combinations, and carries lower AIC and BIC penalties, establishing it as the more promising candidate for partially easing the $H_0$ tension within a modified gravity framework.

Figures

Figures reproduced from arXiv: 2606.22262 by B. Mishra, Kesava Chodavarapu, Rahul Bhagat.

Figure 1
Figure 1. Figure 1: FIG. 1. Contour plot for the combined dataset for the CC, Pan [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Posterior probability distributions of the Hubble con [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Contour plot for the combined dataset for the CC, Pan [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Posterior probability distributions of the Hubble con [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Plot illustrate the inferred [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Variation of [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Contour plot for the combined dataset for the CC, Pan [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Posterior probability distributions of the Hubble con [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗

discussion (0)

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This paper was first reviewed by grok-4.3 on June 26, 2026.