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arxiv: 2607.00169 · v1 · pith:EHVOPZ3Anew · submitted 2026-06-30 · 🌀 gr-qc

Cosmological implications of f(T, B) gravity: constraints from recent observations

Laxmipriya Pati , Santosh V. Lohakare , S. K. Maurya This is my paper

Pith reviewed 2026-07-02 17:34 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(T,B) gravityteleparallel gravitydark energycosmological constraintsHubble tensionphantom divideMCMC analysis
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The pith

A specific power-law f(T,B) gravity model fits combined cosmic chronometer and supernova data better than ΛCDM and suggests reduced Hubble tension.

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

The paper tests whether adding a boundary term to teleparallel gravity can explain the universe's late-time acceleration with a simple power-law extension. It assumes the form f(T, B) = -T + α (-B)^β and runs MCMC fits against cosmic chronometers, Pantheon Plus supernovae, and DESI BAO data. The Akaike criterion indicates the combined CC+PPS set prefers this model over standard ΛCDM. The same runs produce a dynamical crossing of the phantom divide and a lower inferred Hubble constant that moves closer to local measurements.

Core claim

The f(T,B) model with the chosen power-law ansatz reproduces the observed expansion history, yields an improved AIC score on the CC+PPS combination relative to ΛCDM, exhibits phantom-divide crossing, and produces an H0 value that partially relieves the tension between early- and late-time measurements.

What carries the argument

The power-law ansatz f(T, B) = -T + α (-B)^β, which reduces to f(T) or f(R) gravity in limits and supplies the extra degree of freedom needed to drive acceleration while remaining consistent with background data.

If this is right

  • The model produces a dynamical crossing of the phantom divide at late times.
  • It supplies a viable expansion history that matches current background observations.
  • The AIC preference for the model on CC+PPS data indicates a better phenomenological description of late-time acceleration than ΛCDM.
  • The inferred Hubble constant moves closer to local measurements, pointing toward partial relief of the H0 discrepancy.

Where Pith is reading between the lines

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

  • If the boundary term is confirmed as the key addition, similar extensions might unify torsion and curvature descriptions without extra scalar fields.
  • High-redshift BAO or supernova samples could test whether the phantom crossing persists or occurs at a different epoch.
  • The specific power-law choice might be replaced by other functional forms to check whether the improved fit is robust or ansatz-dependent.

Load-bearing premise

The chosen power-law form of f(T, B) is representative enough of the broader theory class that background expansion data alone can meaningfully constrain it and compare it to ΛCDM.

What would settle it

A complete re-analysis of the Hubble tension using the same model but with full CMB and local distance-ladder data that shows the tension remains at the same statistical significance would falsify the alleviation claim.

read the original abstract

In this work, we examine the theoretical framework of modified teleparallel gravity with the inclusion of the boundary term in the action and investigate its cosmological implications by considering the power-law model $f(T, B) = -T + \alpha (-B)^{\beta}$, with the aim of addressing the late-time accelerated expansion and the dark energy. In this context, $T$ denotes the torsion scalar and $B$ represents the boundary term, whose presence allows for departures from standard teleparallel dynamics and provides a unified description that connects torsion and curvature-based formulations, reproducing $f(T)$ and $f(R)$ gravity in appropriate limits. The viability of the model is assessed by confronting its theoretical predictions with observational data while constraining the cosmological and model parameters through a Markov Chain Monte Carlo (MCMC) analysis using cosmic chronometers (CC), the Pantheon Plus sample (PPS), and the DESI baryon acoustic oscillation (BAO) Data Release 2 (DR2) datasets, and comparing its performance with the standard $\Lambda$CDM model. The Akaike Information Criterion (AIC) analysis shows that the combined CC+PPS dataset strongly favors the $f(T, B)$ model, suggesting an improved phenomenological fit to late-time observations relative to $\Lambda$CDM. Our result further shows an alleviation of H0 tensions, although a dedicated analysis is required to establish its full statistical significance. Furthermore, the background cosmological quantities indicate that the model exhibits a dynamical phantom-divide crossing while remaining consistent with late-time observations and yielding a viable expansion history and characteristic dark energy evolution.

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

4 major / 2 minor

Summary. The paper examines a specific power-law model f(T, B) = -T + α (-B)^β in modified teleparallel gravity that incorporates the boundary term B. It performs MCMC constraints on the model parameters together with standard cosmological parameters using cosmic chronometers (CC), Pantheon Plus (PPS), and DESI BAO DR2 datasets, then compares the fit to ΛCDM via the Akaike Information Criterion (AIC). The central claims are that the CC+PPS combination strongly favors the f(T,B) model, that the model alleviates the H0 tension, and that it produces a viable expansion history with a dynamical phantom-divide crossing.

Significance. If the reported AIC preference survives robustness tests against other functional forms and if the MCMC results prove reproducible, the work would supply a concrete two-parameter extension of teleparallel gravity that improves the phenomenological description of late-time expansion relative to ΛCDM on current background data. The inclusion of DESI DR2 adds timeliness. The significance remains limited, however, because the improvement may arise from the added parametric freedom rather than from any independent, parameter-free prediction, and because only background observables are used.

major comments (4)
  1. [Model definition (abstract and §2)] The power-law ansatz f(T, B) = -T + α (-B)^β is introduced without a variational derivation, stability analysis, or comparison to other functional forms (exponential, logarithmic). Because any two-parameter modification to the Friedmann equation can lower χ² on late-time data, the reported AIC preference for CC+PPS may simply reflect the extra degrees of freedom rather than physical content of the boundary term.
  2. [Statistical analysis and AIC comparison (results section)] The statement that 'the combined CC+PPS dataset strongly favors the f(T, B) model' via AIC requires the explicit ΔAIC value, the effective number of parameters, and a quantitative assessment of whether the improvement exceeds the AIC penalty for α and β. No robustness checks against alternative ansätze are shown, undermining the claim that the specific power-law form is preferred.
  3. [H0 results and discussion] The claim of 'alleviation of H0 tensions' is not accompanied by the best-fit H0 value, its uncertainty, or the tension level (in σ) relative to Planck or other early-universe probes. Without these numbers it is impossible to judge whether the alleviation is statistically meaningful or merely a byproduct of the late-time data fit.
  4. [MCMC methodology (§3 or equivalent)] Priors on the model parameters α and β, MCMC convergence diagnostics (Gelman-Rubin statistic or equivalent), and any systematic checks are not reported. These details are load-bearing for the reliability of the constraints and the AIC comparison that constitute the paper's main result.
minor comments (2)
  1. [Notation throughout] Clarify the notation for the torsion scalar T and boundary term B in all equations and text to avoid ambiguity.
  2. [Introduction and model section] Add a brief discussion of the theoretical limits in which the model recovers f(T) or f(R) gravity, with explicit references.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment below, indicating where revisions will strengthen the manuscript and where we maintain the original scope or approach.

read point-by-point responses

  1. Referee: [Model definition (abstract and §2)] The power-law ansatz f(T, B) = -T + α (-B)^β is introduced without a variational derivation, stability analysis, or comparison to other functional forms (exponential, logarithmic). Because any two-parameter modification to the Friedmann equation can lower χ² on late-time data, the reported AIC preference for CC+PPS may simply reflect the extra degrees of freedom rather than physical content of the boundary term.

    Authors: The chosen power-law form is a phenomenological ansatz motivated by its ability to incorporate the boundary term while recovering f(T) and f(R) limits in appropriate regimes. A full variational derivation from a fundamental action is not provided because the focus of the work is on observational viability rather than theoretical construction from first principles. We will add a brief paragraph in §2 discussing the motivation for this ansatz and a qualitative stability consideration. We agree that the AIC improvement must be interpreted in light of the extra parameters and will make this explicit. revision: partial

  2. Referee: [Statistical analysis and AIC comparison (results section)] The statement that 'the combined CC+PPS dataset strongly favors the f(T, B) model' via AIC requires the explicit ΔAIC value, the effective number of parameters, and a quantitative assessment of whether the improvement exceeds the AIC penalty for α and β. No robustness checks against alternative ansätze are shown, undermining the claim that the specific power-law form is preferred.

    Authors: We will report the explicit ΔAIC value, state the effective number of parameters, and provide a quantitative discussion of whether the improvement exceeds the AIC penalty in the revised results section. Robustness checks against other functional forms (e.g., exponential or logarithmic) were outside the scope of the present study, which is restricted to this specific power-law model; we will add a sentence noting this limitation. revision: yes

  3. Referee: [H0 results and discussion] The claim of 'alleviation of H0 tensions' is not accompanied by the best-fit H0 value, its uncertainty, or the tension level (in σ) relative to Planck or other early-universe probes. Without these numbers it is impossible to judge whether the alleviation is statistically meaningful or merely a byproduct of the late-time data fit.

    Authors: The abstract already qualifies the H0 statement by noting that a dedicated analysis is required. In the revised manuscript we will tabulate the best-fit H0 and its uncertainty from the MCMC posterior for the CC+PPS combination. A full σ-level tension calculation against Planck would require joint early- and late-universe data and is left for future work, consistent with the manuscript's stated scope. revision: partial

  4. Referee: [MCMC methodology (§3 or equivalent)] Priors on the model parameters α and β, MCMC convergence diagnostics (Gelman-Rubin statistic or equivalent), and any systematic checks are not reported. These details are load-bearing for the reliability of the constraints and the AIC comparison that constitute the paper's main result.

    Authors: We will include the priors adopted for α and β, the Gelman-Rubin convergence statistics, and a brief description of systematic checks in the methodology section of the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard phenomenological fitting of an explicit ansatz.

full rationale

The paper adopts the power-law ansatz f(T,B)=-T+α(-B)^β by direct statement and performs MCMC parameter estimation against external datasets (CC, PPS, DESI BAO), followed by AIC model comparison to ΛCDM. No derivation chain is claimed that reduces to self-definition, fitted parameters renamed as independent predictions, or load-bearing self-citations. The reported preference and H0 values are explicit outputs of the fit procedure itself, not presented as parameter-free forecasts. This is ordinary model-constraint analysis with no reduction by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the chosen power-law functional form, the assumption that background expansion data alone can validate the model, and standard FLRW cosmology plus MCMC statistical machinery. Two free parameters α and β are introduced and fitted.

free parameters (2)
  • α
    Amplitude parameter in the power-law model, fitted via MCMC to the observational datasets.
  • β
    Exponent parameter in the power-law model, fitted via MCMC to the observational datasets.
axioms (2)
  • domain assumption Background spacetime is described by the flat FLRW metric.
    Standard assumption invoked when deriving the modified Friedmann equations for f(T,B) cosmology.
  • domain assumption MCMC sampling with the listed datasets yields unbiased posterior constraints on the model parameters.
    Implicit in the claim that the data favor the model and alleviate H0 tension.

pith-pipeline@v0.9.1-grok · 5828 in / 1526 out tokens · 24887 ms · 2026-07-02T17:34:24.762407+00:00 · methodology

discussion (0)

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