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arxiv: 2606.19905 · v1 · pith:JZ7YZDVRnew · submitted 2026-06-18 · 🌀 gr-qc

Cosmological Constraints on Minimal Cubic Galileon Models in Teleparallel Gravity

Akbar Davlataliev , Abdurakhmon Nosirov , Odil Yunusov , Bobomurat Ahmedov , Jackson Levi Said This is my paper

Pith reviewed 2026-06-26 16:53 UTC · model grok-4.3

classification 🌀 gr-qc
keywords cubic Galileonteleparallel gravitylate-time accelerationcosmological constraintsHubble tensionBAOPantheon+information criteria
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The pith

Teleparallel cubic Galileon models accommodate late-time cosmic expansion comparably to ΛCDM in some cases.

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

The paper constrains minimal cubic Galileon models inside teleparallel gravity by introducing a single extra parameter b1 that measures departure from the teleparallel equivalent of general relativity. Two scalar potentials (quadratic and exponential) are examined in four combinations of fixed or free b1. Data from Pantheon+ supernovae, cosmic chronometers, SH0ES, and BAO are used to fit the models and compare them with ΛCDM via chi-squared, AIC, and BIC. The fixed-b1 quadratic-potential version yields a lower minimum chi-squared than ΛCDM once BAO are included and receives comparable AIC support, while BIC still prefers the simpler model because of extra parameters.

Core claim

The considered teleparallel cubic Galileon models can accommodate the late-time expansion history, although the statistical preference depends on the choice of potential and on whether b1 is fixed or varied. In particular, the fixed-b1 model with a quadratic potential provides the most competitive fit among the Galileon scenarios when BAO data are included, showing a lower χ²_min than ΛCDM and comparable support according to the AIC criterion. However, the BIC criterion continues to favor the minimal ΛCDM model because of the larger parameter space of the extended models.

What carries the argument

The parameter b1 that encodes deviations from the teleparallel equivalent of general relativity inside the cubic Galileon action, together with quadratic or exponential scalar-field potentials.

If this is right

  • The models remain phenomenologically viable for describing late-time acceleration.
  • Statistical preference among the scenarios varies with the potential form and with whether b1 is fixed or free.
  • BIC continues to select ΛCDM over the Galileon extensions due to the penalty for extra parameters.
  • Any stronger claim that these models resolve the Hubble tension requires additional consistency tests beyond the current data combinations.

Where Pith is reading between the lines

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

  • The competitiveness of the fixed-b1 quadratic case suggests that a discrete choice of b1 may be theoretically preferred and worth testing in other teleparallel extensions.
  • Dependence of the fit quality on the inclusion of BAO indicates that future large-scale-structure surveys could tighten or rule out these scenarios more decisively.
  • If the models continue to fit well, they motivate checking whether the same b1 value also works for early-universe observables such as the CMB power spectrum.

Load-bearing premise

The data sets (Pantheon+, cosmic chronometers, SH0ES, BAO) are assumed to be mutually compatible and free of significant unaccounted systematics that would change the relative chi-squared and information-criterion rankings.

What would settle it

A reanalysis or new data set that drives the minimum chi-squared of every Galileon variant significantly above that of ΛCDM even after BAO are added, or that produces mutually inconsistent best-fit values of b1 across different data combinations.

Figures

Figures reproduced from arXiv: 2606.19905 by Abdurakhmon Nosirov, Akbar Davlataliev, Bobomurat Ahmedov, Jackson Levi Said, Odil Yunusov.

Figure 1
Figure 1. Figure 1: FIG. 1: MCMC corner plot for the cubic Galileon teleparallel cosmology with quadratic effective potential [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: MCMC corner plot for the cubic Galileon teleparallel cosmology with exponential effective potential [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: MCMC corner plot for the cubic Galileon teleparallel cosmology with quadratic effective potential [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: MCMC corner plot for the cubic Galileon teleparallel cosmology with exponential effective potential [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: MCMC corner plot for the standard ΛCDM cosmology, adopted as the reference model for the model comparison [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Whisker plot of [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
read the original abstract

Cubic Galileon cosmological models provide a well-motivated framework for investigating late-time cosmic acceleration beyond the standard $\Lambda$CDM paradigm. In this work, we study observational constraints on cubic Galileon models within the teleparallel gravity framework, where deviations from the standard teleparallel equivalent of general relativity are encoded through the model parameter $b_1$. We consider two scalar-field potentials, namely quadratic and exponential potentials, and analyze four representative scenarios: quadratic and exponential potentials with $b_1$ treated as a free parameter, together with the corresponding cases in which $b_1=2$ is fixed. Using the $\text{Pantheon}^+$ Type Ia supernova sample, cosmic chronometer measurements, SH0ES information, and baryon acoustic oscillation data, we constrain the cosmological and model parameters and compare the observational viability of the different scenarios. We find that the considered teleparallel cubic Galileon models can accommodate the late-time expansion history, although the statistical preference depends on the choice of potential and on whether $b_1$ is fixed or varied. In particular, the fixed-$b_1$ model with a quadratic potential provides the most competitive fit among the Galileon scenarios when BAO data are included, showing a lower $\chi^2_{\min}$ than $\Lambda$CDM and comparable support according to the AIC criterion. However, the BIC criterion continues to favor the minimal $\Lambda$CDM model because of the larger parameter space of the extended models. These results suggest that teleparallel cubic Galileon cosmologies remain phenomenologically viable, while a stronger claim regarding the Hubble tension requires further consistency tests.

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

1 major / 0 minor

Summary. The manuscript examines cosmological constraints on minimal cubic Galileon models in teleparallel gravity, where deviations are parameterized by b1. It considers quadratic and exponential potentials in four scenarios (b1 free or fixed to 2), fitting to Pantheon+ supernovae, cosmic chronometers, SH0ES, and BAO data. The central claim is that these models accommodate the late-time expansion history, with the fixed-b1 quadratic potential yielding the most competitive fit among Galileon cases (lower χ²_min than ΛCDM with BAO included, comparable AIC but BIC favoring ΛCDM due to extra parameters), indicating phenomenological viability while noting that stronger claims on the Hubble tension require further tests.

Significance. If the statistical comparisons hold after addressing data compatibility, the work demonstrates that teleparallel cubic Galileon models remain viable extensions capable of competitive fits to expansion history data, with explicit AIC/BIC rankings highlighting the parameter-count penalty relative to ΛCDM. This adds concrete numerical evidence to the literature on teleparallel modifications without introducing new entities or ad-hoc axioms beyond standard parameter fitting.

major comments (1)
  1. The joint likelihood analysis of Pantheon+, cosmic chronometers, SH0ES, and BAO implicitly assumes statistical compatibility without reported tension statistics, separate fits, or covariance re-estimation. This assumption underpins the claim that the fixed-b1 quadratic model provides the most competitive fit (lower χ²_min than ΛCDM with BAO), as unmodeled systematics could shift relative χ² values and alter AIC/BIC rankings.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comment. We respond to the major comment below.

read point-by-point responses

  1. Referee: The joint likelihood analysis of Pantheon+, cosmic chronometers, SH0ES, and BAO implicitly assumes statistical compatibility without reported tension statistics, separate fits, or covariance re-estimation. This assumption underpins the claim that the fixed-b1 quadratic model provides the most competitive fit (lower χ²_min than ΛCDM with BAO), as unmodeled systematics could shift relative χ² values and alter AIC/BIC rankings.

    Authors: We acknowledge that explicit checks for inter-dataset compatibility would strengthen the presentation. Our analysis follows the standard practice in the field of performing joint fits to these commonly combined datasets without additional covariance adjustments. To address the concern, the revised manuscript will include the individual χ² contributions from each dataset for the best-fit models of the fixed-b1 quadratic case and ΛCDM, together with a short discussion of dataset compatibility based on the separate constraints already obtained during the MCMC runs. This addition will allow readers to evaluate whether systematics could affect the reported χ²_min differences and information criteria rankings, while preserving the core result that the model remains viable under the joint likelihood. revision: partial

Circularity Check

0 steps flagged

No significant circularity; standard observational constraints on fitted models

full rationale

The paper performs standard Bayesian parameter estimation and model comparison (χ², AIC, BIC) on teleparallel cubic Galileon cosmologies against external datasets (Pantheon+, cosmic chronometers, SH0ES, BAO). The claim that models 'can accommodate the late-time expansion history' is the direct numerical outcome of these fits, not a derivation presented as first-principles or independent of the input data. No self-definitional steps, fitted inputs renamed as predictions, load-bearing self-citations, uniqueness theorems, or ansatz smuggling appear in the provided text. The analysis is self-contained against the cited external benchmarks, which is the expected non-circular outcome for a constraints paper.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim of phenomenological viability rests entirely on the ability to fit the model parameters to the observational data sets; there are no independent derivations or external validations for the specific values or forms beyond the fits themselves.

free parameters (3)
  • b1
    Parameter controlling deviation from standard teleparallel gravity, fitted or fixed in different scenarios
  • scalar field potential parameters
    Parameters in quadratic and exponential potentials, fitted to data
  • cosmological parameters (e.g. matter density, Hubble constant)
    Standard parameters adjusted to match observations
axioms (2)
  • domain assumption The background cosmology follows the Friedmann-Lemaître-Robertson-Walker metric in teleparallel gravity
    Invoked to derive the expansion history equations for the models
  • domain assumption The cubic Galileon action is appropriately formulated in the teleparallel framework
    Basis for the model definition and the role of b1

pith-pipeline@v0.9.1-grok · 5845 in / 1668 out tokens · 51531 ms · 2026-06-26T16:53:03.147905+00:00 · methodology

discussion (0)

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