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Higgs-like inflation in scalar-torsion $f(T,\phi)$ gravity in light of ACT-SPT-DESI constraints

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Higgs-like inflation in scalar-torsion gravity remains viable under the latest Planck, ACT, DESI, and BICEP/Keck constraints, predicting a scalar spectral index ns≈0.968–0.977 and a tensor-to-scalar ratio r≈0.009–0.039.

desk verdict Plausible framework, timely topic, but the printed analytic formulas contradict the paper's own tables, and the slow-roll claims are at odds with its own figures. read the letter →

arxiv 2512.24502 v2 pith:SDUVJLGK submitted 2025-12-30 gr-qc astro-ph.COhep-phhep-th

Nitesh Kumar , Giovanni Otalora , Rodrigo Reyes , Bastian Espinoza , Manuel Gonzalez-Espinoza , Emmanuel N. Saridakis This is my paper · ORCID
classification gr-qcastro-ph.COhep-phhep-th MSC 83F0583D05 PACS 98.80.Cq04.50.Kd04.50.-h98.80.Es
keywords Higgs-likeinflationscalar-torsiongravityf(Tφ)scalarspectralindextensor-to-scalarratioteleparallelslow-rollapproximationCMBconstraints
verification ladder T0 review T1 audit T2 compute T3 formal

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 argues that Higgs-like inflation, when implemented in scalar-torsion f(T,φ) gravity rather than standard curvature-based gravity, is fully consistent with current cosmological data. By assuming a quartic Higgs potential and a power-law nonminimal coupling to torsion, the authors derive closed-form expressions for the inflationary observables in the dominant-coupling regime and confirm them numerically beyond that regime. The model naturally produces the higher value of the scalar spectral index preferred by ACT and DESI, while keeping the tensor-to-scalar ratio below the BICEP/Keck bound. If correct, it provides a torsion-based alternative to plateau-type inflation models that are increasingly disfavored by recent data, and it predicts specific, testable signatures in the tensor and running sectors.

What carries the argument

The central object is the scalar-torsion action f(T,ϕ)=−M_Pl²T/2−G(T)F(ϕ)−V(ϕ) with a power-law ansatz G(T)∼T^s, a Higgs-like coupling F(ϕ)=ξϕ^c, and the quartic potential V(ϕ)=λ(ϕ²−ν²)²/4. In the dominant-coupling (high-energy) regime, where T≪|GF|C(T)/M_Pl², the slow-roll equations simplify to yield closed-form relations between the number of e-folds N and the observables ns and r, together with explicit expressions for the couplings λ and ξ fixed by the observed amplitude of scalar perturbations. The key mechanism is the torsion-induced correction 2ηR in the scalar spectral index and the modified consistency relation in the tensor sector, which shift predictions relative to curvature-base

What would settle it

A future CMB experiment that measures r with precision σ(r)∼10⁻³ would decisively test the model: if r is found to exceed the predicted upper envelope of about 0.04 at N=60, or if ns is measured outside the 0.968–0.977 band at high significance, the scalar-torsion Higgs scenario would be excluded. Additionally, a full numerical integration of the background and perturbation equations without the slow-roll approximation, using the same action, would reveal whether the analytic spectra remain accurate when ηR becomes large.

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Extended reading notes

Core claim

The core claim is that Higgs-like inflation in the general scalar-torsion f(T,φ) framework remains compatible with the tightest available CMB and large-scale-structure constraints. In the dominant-coupling regime, where the scalar-torsion interaction dominates over the Einstein-Hilbert term, the authors obtain analytical formulas for ns(N), r(N), and the running αs(N). For 50–60 e-folds and suitable choices of the parameters c, s, and γ, the model predicts ns≈0.968–0.977 and r≈0.009–0.039, which falls inside the 68% confidence contour of the combined Planck 2018, ACT DR6, DESI DR1, and BICEP/Keck datasets. Numerical integration of the slow-roll equations beyond the dominant-coupling approxim

Load-bearing premise

The entire comparison with observations rests on the scalar and tensor power spectra taken from previous work by the same group, and on the validity of the slow-roll approximation at horizon crossing; the paper itself shows ηR reaching values well above unity near the end of inflation, so slow-roll may not hold throughout the full trajectory.

Editorial extensions

If this is right

  • If the model is correct, the upward shift of ns to ≈0.974 preferred by ACT and DESI is no longer an obstacle for Higgs-type inflation; torsion corrections naturally raise ns relative to plateau models.
  • The predicted tensor-to-scalar ratio r≈0.009–0.039 lies within reach of upcoming CMB polarization experiments like Simons Observatory, CMB-S4, and LiteBIRD, providing a concrete observational test.
  • The modified consistency relation r=8(−nT−3δ_{f,T}) implies that a measurement of r and nT together could distinguish torsion-based inflation from standard single-field inflation.
  • The model fixes the effective self-coupling λ at roughly 10⁻¹⁵ and the nonminimal coupling ξ at order 0.1–0.01 in the numerically explored range, which can be compared with particle-physics expectations for a Higgs-like field.
  • The running of the scalar spectral index αs is predicted to be negative and of order −(4 to −6)×10⁻⁴, a small but potentially measurable signature.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If future data continue to push ns toward 1, the allowed parameter space shrinks to a narrow band near c≈0.25 and s≈0.51–0.55, which may indicate fine-tuning; a precision measurement of ns beyond current errors would reveal how much tuning is needed.
  • The dominant-coupling regime involves trans-Planckian field values (ϕ∼100 M_Pl as shown in Fig. 6), which raises effective-field-theory concerns; the authors' unitarity discussion for a generic Higgs-like inflaton may not fully settle whether the slow-roll trajectory can be consistently embedded in a UV-complete theory.
  • The paper leaves open the computation of non-Gaussianities and reheating dynamics within this scalar-torsion framework; those extensions could provide additional, independent observational signatures.
  • Because the power spectra are imported from earlier work, a direct re-derivation of P_s(k) and P_T(k) from the second-order action—without the slow-roll truncation—would be a natural check of the robustness of the claimed compatibility.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper studies Higgs-like inflation in scalar-torsion f(T,φ) gravity with action (2.13), specializing to G(T) ∼ T^s, F(φ)=ξφ^c and a quartic symmetry-breaking potential (Sec. IV). Working in the slow-roll approximation and using primordial spectra taken from the authors’ earlier papers [70,73], it derives closed-form expressions for n_s, α_s and r in the dominant-coupling regime (Eqs. 4.11–4.13), and then numerically integrates the slow-roll equations beyond that regime (Sec. V). The predictions are compared with Planck, ACT DR6, DESI DR1 and BICEP/Keck constraints, and the paper concludes that Higgs-like inflation in f(T,φ) gravity is fully consistent with current bounds and naturally accommodates the upward shift in n_s.

Significance. If the results were correct, this would be a useful contribution: it would show that a torsion-based modified-gravity inflationary model remains viable under the updated n_s–r constraints and offers distinctive tensor-sector and running predictions. The manuscript is clearly organized, provides explicit tables (Tables I–II) and goes beyond the dominant-coupling approximation numerically. However, the central numerical claims are not reproducible from the printed analytic formulas, and the slow-roll consistency of the calculation is not established. The claimed consistency with ACT-SPT-DESI data is therefore not yet supported.

major comments (3)
  1. [§IV, Table I, Eqs. (4.11)–(4.13)] Direct substitution of Table I inputs into the printed formulas does not reproduce the table. For c=0.2479, s=0.5110, N_*=60, Eq. (4.13) with \tilde d from (4.7) gives r≈0.058, while Table I lists r=0.0164. Moreover, Eq. (4.11) has an explicit 1/N_* dependence, yet Table I lists identical n_s values at N=50 and N=60 for every parameter row (e.g. 0.9708 in both columns for c=0.2479); Table II shows the same pattern. This indicates that the analytic formulas are not the expressions used to generate the tables and figures that support the abstract’s consistency claim. The mismatch must be resolved, not only cosmetically, because the headline numbers (n_s≈0.968–0.977, r≈0.009–0.039) all rest on these calculations.
  2. [§V, Fig. 7; §III.A, Eqs. (3.9)–(3.16)] The scalar and tensor power spectra used for n_s and r are first-order slow-roll expressions valid only for |η_R|≪1. Figure 7 shows η_R reaching values around 12 near N=0, and Fig. 3 also shows η_R exceeding unity, while the text and captions repeatedly assert that ϵ,|η_R|≪1. Because the number of e-folds N_* is computed by integrating the slow-roll equations from N=0, a region with |η_R|≫1 affects the resulting φ(N_*) and hence the horizon-crossing predictions. The authors need to show that this region is irrelevant to the quoted observables, or re-derive the spectra beyond first order in slow roll.
  3. [§IV–V, Figs. 1 and 4] The central statement that the model is “fully consistent” with Planck/ACT/DESI/BICEP-Keck rests on visually comparing hand-selected curves with contour plots. The parameters c, s, γ and N_* are varied freely, and no likelihood, χ², or posterior is computed. With several free parameters, the existence of points inside a 68% contour is not a statistical test of consistency. A quantitative comparison (even a simple χ² or profile likelihood) and a statement of which parameter region is observationally allowed are needed before the consistency claim can be evaluated.
minor comments (5)
  1. [Title/Abstract] The title says ACT-SPT-DESI constraints, and the Introduction cites SPT-3G [9], but the combined constraints used in the analysis are Planck, ACT DR6, DESI BAO and BICEP/Keck. Please clarify the role of SPT data.
  2. [Fig. 2 caption] The caption states “The blue contours show results from Planck 2018 … while the blue contours represent the joint constraints”; the second instance should presumably be “orange”.
  3. [§V and Fig. 7] The caption and text assert that ϵ and η_R remain “much smaller than unity,” but the plotted η_R axis reaches 12. The caption must be corrected to match the figure, and the discussion should address the large-η_R region near N=0.
  4. [Eq. (4.12)] The running α_s is written as the same negative bracket divided by N_*^2. If n_s−1 ≈ −A/N_*, then d(n_s−1)/dN = A/N_*^2, so the sign appears inconsistent with Eq. (4.11); please check this relation.
  5. [Various] Typographical errors include “regieme” (p.17), “unitaity” (p.21), “throught” (p.17), and “Fig. ,Fig. 2” (p.14). Please proofread.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the inflationary observables are derived from stated general power spectra and compared with external data; parameter scanning and slow-roll concerns are correctness issues, not definitional input-output equivalence.

full rationale

The derivation chain is not circular. The inflationary observables follow from the general scalar/tensor power spectra (Eqs. 2.45-2.57 and 3.9-3.16), which are imported from refs. [70,73] by overlapping authors. This is a self-citation and it is load-bearing for the numbers, but the cited results are general, parameter-free slow-roll spectra with stated assumptions (uniform-field gauge, linear perturbations, slow-roll truncation), not fits to the target observables; under the review rules such citations count as independent evidence rather than circularity. The paper also sketches the perturbation action from which those spectra arise. The subsequent Higgs-like specialization (quartic potential, F = xi phi^c, G ~ T^s) is algebra from those spectra, not a renaming of the input. lambda is fixed by the Planck scalar amplitude, while ns and r depend on c,s,N and are compared with external Planck/ACT/DESI/BICEP contours; scanning c,s,gamma is standard parameter-space exploration. The 'consistent with data' claim is an existence proof with tuned parameters rather than a sharp out-of-sample prediction, which weakens its force, but that is not a definitional circularity. Two correctness flags should be kept separate from circularity: the text asserts |eta_R| << 1 while its own Fig. 7 shows eta_R up to ~12 near N=0 (and Fig. 3 up to ~1.4), questioning slow-roll validity; and Eq. (4.13) evaluated with Table I inputs (c=0.1100, s=0.5110, N=60) gives r ~ 0.029 versus the listed 0.0092. The paper also states in Sec. IV that phi is not the SM Higgs, limiting the 'Higgs-like' label. None of these exhibits a predicted quantity equal by construction to a fitted input.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the prior power-spectra results [70,73], the slow-roll approximation, the assumed power-law forms G(T)=T^s and F(φ)=ξφ^c, and the free parameters c, s, γ, N* which are tuned to match the data. No new particles or forces are introduced.

free parameters (4)
  • c = 0.1100–0.3857 (analytic); 0.2150–0.4499 (numerical)
    Power of φ in the non-minimal coupling F(φ)=ξφ^c. Scanned to place the predicted (ns,r) inside the observed confidence regions (Table I, Fig. 1).
  • s = 0.5005–0.5495
    Power of T in G(T)=T^s. Scanned in a narrow band just above s=1/2; the model requires s>1/2, and the chosen values are tuned to match data (Table I, Fig. 1).
  • γ = 1e-12 to 3e-9
    Coupling parameter in the numerical section (γ=λ/(d ξ^{1/(1-s)})). Scanned to explore regimes and to keep predictions within the observed 2σ region (Table II, Fig. 4c).
  • N* = 50–60
    Number of e-folds at horizon crossing. Taken in the standard range; the results vary with N*, and the tables list values at N=50 and N=60.
assumptions (5)
  • domain assumption The power spectra of curvature and tensor perturbations in f(T,φ) gravity, Eqs. (2.45)–(2.57) and (3.9)–(3.16), are correct
    The paper takes these spectra from the authors' earlier papers [70,73] and does not re-derive them; they are load-bearing for all predictions of ns, r, and αs.
  • domain assumption The slow-roll approximation is valid at horizon crossing for the parameter ranges explored
    The analytic and numerical results use the slow-roll truncation. The paper's own Fig. 7 shows ηR approaching 12 near N=0, so the validity of this assumption for the full inflationary interval is not established.
  • domain assumption The Higgs-like potential V(φ)=λ/4(φ^2−ν^2)^2 with ν negligible in the large-field regime φ^2≫ν^2
    The analysis uses the quartic potential and drops the vacuum expectation value; this is a standard simplification but not derived in the paper.
  • ad hoc to paper The power-law forms G(T)=T^s and F(φ)=ξφ^c with s>1/2
    These functional forms are assumed to enable analytic progress. The narrow range of s just above 1/2 is not motivated by any underlying theory.
  • domain assumption The dominant-coupling (high-energy) regime condition T≪|G(T)F(φ)C(T)|/M_Pl^2
    Used to derive the leading-order expressions (3.24)–(3.31). The numerical section relaxes this, but the analytic results in Section IV rely on it.

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Pith. "Pith review of Higgs-like inflation in scalar-torsion $f(T,\phi)$ gravity in light of ACT-SPT-DESI constraints." pith.science (2026). https://pith.science/paper/SDUVJLGK

@misc{pith2026251224502,
  author       = {Pith},
  title        = {Pith review of: Higgs-like inflation in scalar-torsion $f(T,\phi)$ gravity in light of ACT-SPT-DESI constraints},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SDUVJLGK}},
  note         = {Machine review of arXiv:2512.24502}
}
abstract

We study Higgs-like inflation in the framework of scalar-torsion gravity, focusing on the general class of $f(T,\phi)$ theories in which gravitation is mediated by torsion rather than curvature. Motivated by the increasing precision of cosmic microwave background and large-scale-structure observations, we examine whether Higgs-like inflation remains compatible with current data in this extended gravitational setting. Working within the slow-roll approximation, we analyze the inflationary dynamics both analytically and numerically. In the dominant-coupling regime we derive closed-form expressions for the scalar spectral index and the tensor-to-scalar ratio as functions of the number of e-folds, and we subsequently relax this assumption by numerically solving the slow-roll equations. Confrontation with the latest constraints from Planck 2018, ACT DR6, DESI DR1, and BICEP/Keck shows that Higgs-like inflation in $f(T,\phi)$ gravity is fully consistent with current bounds, naturally accommodating the preferred shift in the scalar spectral index and leading to distinctive tensor-sector signatures.

Figures

Figures reproduced from arXiv: 2512.24502 by the authors.

Figure 1
Figure 1. FIG. 1. Contour plots of the scalar spectral index [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Constraints on the spectral index [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Behavior of the analytically solved background inflationary quantities in our Higgs-like inflation model with [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Constraints in the [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Constraints in the [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Parametric plots showing the evolution of the auxiliary variable [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Behavior of the background inflationary quantities in our Higgs-like inflation model with [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.