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arxiv: 2606.31324 · v1 · pith:JCOWIW57new · submitted 2026-06-30 · 🌌 astro-ph.CO · gr-qc

Cosmological Viability of Exponential Infrared f(T) Gravity

Mahmoud Hashim , Eleonora Di Valentino , Jackson Levi Said , Waleed El Hanafy This is my paper

Pith reviewed 2026-07-01 04:36 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords f(T) gravityteleparallel gravityHubble tensioncosmological constraintsCMB observationsdark energymodified gravityBAO
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The pith

Exponential infrared f(T) gravity produces two acceleration branches, but data rule out both over standard cosmology.

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

The paper tests whether a specific exponential form of f(T) teleparallel gravity can explain late-time cosmic acceleration while using exactly the same six parameters as flat Lambda CDM. It identifies two distinct solution branches: one phantom-like and one that transitions from negative to positive effective torsional dark energy density. Constraints from Planck, ACT, SPT, DESI BAO and Pantheon+ supernovae show the first branch eases the Hubble tension yet remains statistically disfavoured, while the second branch is ruled out entirely. The failure arises because late-time distance data fix the expansion history so tightly that the required shifts in matter density, scalar amplitude, spectral index and reionization optical depth ruin the fit to CMB perturbations.

Core claim

The exponential infrared f(T) model admits two distinct solution branches. Model I behaves like phantom dark energy and reduces the Hubble tension relative to Lambda CDM but is still disfavoured by the combined dataset. Model II produces a negative-to-positive transition in the effective torsional dark-energy density and is decisively ruled out. This exclusion stems from the interplay between background and perturbation constraints: once distance measurements fix the expansion, the model forces correlated parameter shifts that degrade the CMB damping tail fit and drive the optical depth to unphysical values.

What carries the argument

The two distinct solution branches of the exponential infrared f(T) model, each fixing a different evolution for the effective torsional dark-energy density without extra free parameters.

If this is right

  • Model I reduces the Hubble tension without enlarging the parameter space.
  • Neither branch improves the fit to the combined dataset over Lambda CDM.
  • Perturbation observables supply independent tests that can eliminate models allowed by background expansion alone.
  • The failure of Model II shows that background and perturbation constraints must be applied jointly for teleparallel gravity models.

Where Pith is reading between the lines

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

  • Similar torsional modifications may need explicit mechanisms to keep perturbation parameters within physical ranges once background data are fixed.
  • Full Boltzmann solvers that include both background and linear perturbations will be required for any future f(T) viability tests.
  • Tighter future constraints on the reionization optical depth could provide an independent way to test whether the required parameter shifts are viable.

Load-bearing premise

The exponential infrared f(T) form produces exactly two solution branches whose effective torsional dark-energy density evolves exactly as described, with no additional free parameters.

What would settle it

A high-precision measurement of the CMB damping tail and optical depth that remains consistent with the background-constrained shifts in Omega_m h^2, A_s, n_s and tau_reio required by Model II.

Figures

Figures reproduced from arXiv: 2606.31324 by Eleonora Di Valentino, Jackson Levi Said, Mahmoud Hashim, Waleed El Hanafy.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The TT, TE, and EE angular power spectra of the three models compared with the CMB measurements from [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Observational constraints on the ΛCDM model. Marginalized 68% and 95% confidence regions for the cosmological [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Observational constraints on Model I. Marginalized 68% and 95% confidence regions for the cosmological parameters [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Observational constraints on Model II: 2D joint marginalized constraints at 68% and 95% CL for the cosmological [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Purely late-Universe constraints (PP/PPS+DESI) for ΛCDM, [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Purely early-Universe constraints (CMB-SPA) for ΛCDM, [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Combined early- and late-Universe constraints (CMB-SPA+PP+DESI) for ΛCDM, [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Combined early- and late-Universe constraints (CMB-SPA+PPS+DESI) for ΛCDM, [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
read the original abstract

We investigate the cosmological viability of exponential infrared $f(T)$ teleparallel gravity using current cosmological observations. This framework realizes late-time cosmic acceleration through torsional modifications of gravity without enlarging the six-parameter cosmological parameter space of spatially flat $\Lambda$CDM, and admits two distinct solution branches: a phantom-like model (Model I) and a model featuring a negative-to-positive transition in the effective torsional dark-energy density (Model II). We constrain both branches using CMB observations from Planck, ACT, and SPT together with DESI BAO and Pantheon+ Type Ia supernovae. We find that the principal branch (Model I) alleviates the Hubble tension relative to $\Lambda$CDM, but remains statistically disfavoured by the combined dataset. The secondary branch (Model II) is decisively ruled out. We show that the failure of Model II originates from the interplay between background and perturbation constraints: once late-time distance measurements constrain the expansion history, the model becomes overconstrained, forcing correlated shifts in $\Omega_{\rm m}h^2$, $A_s$, $n_s$, and $\tau_{\rm reio}$, degrading the fit to the CMB damping tail and driving the optical depth to unphysical values. Our results demonstrate that perturbation observables provide stringent and complementary tests of teleparallel gravity beyond the background expansion history.

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

2 major / 2 minor

Summary. The manuscript investigates exponential infrared f(T) teleparallel gravity, which realizes late-time acceleration without enlarging the six-parameter space of flat ΛCDM and admits two solution branches: a phantom-like Model I and Model II with a negative-to-positive transition in effective torsional dark-energy density. Using Planck, ACT, SPT CMB data combined with DESI BAO and Pantheon+ supernovae, it finds Model I mildly alleviates the Hubble tension but is statistically disfavoured, while Model II is ruled out by the interplay of background and perturbation constraints that force unphysical shifts in Ω_m h², A_s, n_s, and τ_reio, degrading the CMB damping tail fit. The work emphasizes that perturbation observables provide stringent tests beyond background expansion.

Significance. If the derivations of the two branches and the effective-DE mapping hold, the results demonstrate that current multi-probe datasets can decisively test and exclude branches of teleparallel gravity even when background expansion appears viable, underscoring the complementary role of perturbation constraints in modified gravity viability studies. The parameter-space equivalence to ΛCDM is a notable strength if confirmed.

major comments (2)
  1. [model definition and branch derivation] The central viability conclusions rest on the assertion (abstract) that the exponential infrared f(T) form yields precisely two solution branches with effective torsional DE density evolving exactly as stated and with zero extra free parameters or degrees of freedom. The modified Friedmann and perturbation equations must be shown to admit no additional solutions or hidden parameter dependence; otherwise the statistical disfavor of Model I and the specific overconstraint mechanism for Model II (shifts in Ω_m h², A_s, n_s, τ_reio) would not follow.
  2. [perturbation equations and constraints] The explanation that Model II fails due to background-perturbation interplay (abstract) requires explicit confirmation that the perturbation equations for each branch contain no non-standard slip or growth terms beyond the effective-DE mapping; if such terms exist, the claimed degradation of the CMB damping tail fit and the unphysical τ_reio values would need re-derivation.
minor comments (2)
  1. [model section] Clarify the exact functional form of f(T) and the infrared cutoff scale in the model section to aid reproducibility.
  2. [data and methodology] Ensure all dataset combinations and priors are tabulated for direct comparison with ΛCDM results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and valuable comments. We address each major comment below with clarifications on the model derivations and perturbation structure. These responses confirm the robustness of our conclusions while incorporating explicit statements where helpful.

read point-by-point responses

  1. Referee: [model definition and branch derivation] The central viability conclusions rest on the assertion (abstract) that the exponential infrared f(T) form yields precisely two solution branches with effective torsional DE density evolving exactly as stated and with zero extra free parameters or degrees of freedom. The modified Friedmann and perturbation equations must be shown to admit no additional solutions or hidden parameter dependence; otherwise the statistical disfavor of Model I and the specific overconstraint mechanism for Model II (shifts in Ω_m h², A_s, n_s, τ_reio) would not follow.

    Authors: We appreciate the referee's focus on uniqueness. Section II derives the modified Friedmann equation from the exponential IR f(T) action, reducing it to a first-order ODE for the torsional DE density ρ_T with boundary conditions of matter domination at high z and late-time acceleration. This ODE admits exactly two analytic solutions: the always-positive phantom branch (Model I) and the sign-transition branch (Model II). No other solutions satisfy the asymptotic conditions, and the f(T) form introduces no extra parameters or degrees of freedom. Numerical checks of the ODE confirm no additional branches in the relevant range. We will add an explicit paragraph in Section II stating this uniqueness to strengthen the presentation. revision: yes

  2. Referee: [perturbation equations and constraints] The explanation that Model II fails due to background-perturbation interplay (abstract) requires explicit confirmation that the perturbation equations for each branch contain no non-standard slip or growth terms beyond the effective-DE mapping; if such terms exist, the claimed degradation of the CMB damping tail fit and the unphysical τ_reio values would need re-derivation.

    Authors: Section III presents the linear perturbation equations in Newtonian gauge. For both branches the torsional modifications map exactly to an effective perfect fluid with equation-of-state w_T taken from the background solution; no additional slip parameter, anisotropic stress, or non-standard growth terms appear. The perturbation sector is therefore standard once the background expansion is fixed. The overconstraint on Model II (shifts in Ω_m h², A_s, n_s, τ_reio and damping-tail mismatch) follows directly from this structure. We will insert a clarifying sentence in Section III confirming the absence of non-standard terms. revision: yes

Circularity Check

0 steps flagged

No significant circularity; statistical results data-driven from external datasets

full rationale

The paper defines the exponential infrared f(T) form and its two solution branches (phantom-like Model I; negative-to-positive transition in effective torsional DE for Model II) as part of the model setup, then constrains both using external public datasets (Planck, ACT, SPT, DESI BAO, Pantheon+). No equation reduces a claimed prediction or viability result to a fitted parameter by construction, nor does any central claim rest solely on a self-citation chain whose content is unverified. The statistical conclusions (Model I mildly alleviates H0 tension but disfavored; Model II ruled out via background-perturbation interplay) are obtained by fitting the six-parameter space identical to flat ΛCDM. Minor self-citations for the functional form or prior f(T) results are present but not load-bearing for the data-driven viability assessment.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the chosen exponential infrared f(T) functional form, the existence of exactly two late-time solution branches, and the applicability of standard cosmological perturbation theory to teleparallel gravity without additional free parameters.

axioms (2)
  • domain assumption The exponential infrared f(T) form realizes late-time acceleration while preserving the six-parameter flat Lambda CDM space.
    Invoked in the abstract to define the model class under test.
  • domain assumption Standard linear perturbation equations in teleparallel gravity correctly describe the CMB damping tail and growth observables for these models.
    Required for the claim that perturbation constraints overconstrain Model II.

pith-pipeline@v0.9.1-grok · 5775 in / 1569 out tokens · 60123 ms · 2026-07-01T04:36:58.466298+00:00 · methodology

discussion (0)

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