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T0 review · grok-4.3

The Cosh-type model in f(Q,φ) gravity with nonminimal coupling predicts ns ≈ 0.966 and r ≈ 0.018 at 60 e-folds, matching Planck data.

2026-05-07 14:56 UTC

load-bearing objection The paper constrains ξ in f(Q,φ) inflation to fit Planck data for two potentials but likely applies unmodified slow-roll formulas for ns and r. the 2 major comments →

arxiv 2604.26156 v1 submitted 2026-04-28 gr-qc

Inflationary Scenarios in f(Q,φ) Gravity with Scalar Field Coupling

F. Mavoa , M.B. Barry , R. Ndioukane , M.G. Ganiou , F.K. Ahloui This is my paper
classification gr-qc
keywords f(Q,φ) gravitynonminimal couplinginflationscalar spectral indextensor-to-scalar ratioCosh potentialDe Sitter inflation
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.

This paper studies inflationary models inside f(Q,φ) gravity where a scalar field couples nonminimally to the nonmetricity scalar. It shows that De Sitter inflation produces acceptable spectra only inside a narrow window of the coupling strength ξ. The Cosh-type potential, by contrast, yields a scalar spectral index that rises and a tensor-to-scalar ratio that falls with increasing e-fold number, landing inside current observational bounds at N = 60. A reader would care because the coupling supplies an extra handle that can bring modified-gravity inflation into agreement with data without fine-tuning the potential itself.

Core claim

In the Cosh-type inflationary model within f(Q,φ) gravity, the tensor-to-scalar ratio decreases while the scalar spectral index increases with the number of e-folds N. For N = 60 the model gives ns ≈ 0.965–0.967 and r ≈ 0.017–0.018, values compatible with Planck constraints. In the De Sitter case the same coupling raises ns and lowers r, restricting viable ξ to the interval 10^{-3} ≲ ξ ≲ 10^{-2} and imposing an upper bound ξ < κ/(2p).

What carries the argument

The nonminimal coupling term between the scalar field and the nonmetricity scalar Q, which enters the slow-roll parameters and thereby controls the tilt of the scalar spectrum and the amplitude of tensor modes.

Load-bearing premise

The chosen functional forms for f(Q,φ) and the inflationary potentials, together with the validity of the slow-roll approximation, remain accurate throughout the entire inflationary phase.

What would settle it

A future measurement showing r > 0.02 or ns < 0.96 at the pivot scale for N = 60 would rule out the Cosh-type realization in this framework.

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

If this is right

  • Raising the coupling ξ increases ns and decreases r in the De Sitter branch.
  • The Cosh model stays inside observational windows for a range of N around 60.
  • An upper limit ξ < κ/(2p) follows from demanding a consistent background evolution.
  • Viable spectra appear only inside a restricted interval of ξ for the De Sitter potential.

Where Pith is reading between the lines

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

  • The same coupling could be tested on other potentials to see whether the narrow ξ window is generic or potential-specific.
  • Future CMB polarization data could tighten the bound on ξ beyond the current 10^{-3}–10^{-2} interval.
  • The post-inflationary reheating phase in the same f(Q,φ) action would need to produce the observed radiation temperature to close the model.
  • The mechanism offers a way to embed standard slow-roll results as the limit of vanishing coupling.

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 / 2 minor

Summary. The manuscript investigates inflationary scenarios in f(Q, φ) gravity incorporating a nonminimal coupling ξ between the scalar field and the nonmetricity scalar Q. For De Sitter inflation, it identifies a restricted range 10^{-3} ≲ ξ ≲ 10^{-2} yielding ns and r compatible with Planck data, with ns increasing and r decreasing with ξ, and derives a theoretical upper bound ξ < κ/(2p) (e.g., ξ < 0.00833 for κ=1, p=60). For the Cosh-type potential, it reports that ns increases and r decreases with the number of e-folds N, predicting ns ≈ 0.965-0.967 and r ≈ 0.017-0.018 at N=60 in excellent agreement with observations.

Significance. If the slow-roll parameters and perturbation spectra are correctly derived within the modified f(Q, φ) framework, the results would demonstrate that the nonminimal coupling ξ offers a tunable mechanism to bring inflationary predictions into agreement with current CMB constraints, distinguishing this symmetric teleparallel model from standard GR or minimally coupled cases. The explicit ξ and N dependence provides falsifiable trends that could be tested against future data releases.

major comments (2)
  1. Abstract and Cosh-type model analysis: The central claim that the Cosh-type model yields ns ≈ 0.965-0.967 and r ≈ 0.017-0.018 at N=60 in excellent agreement with Planck data rests on the computation of these observables. In f(Q, φ) gravity with nonminimal ξ coupling, the background equations and scalar/tensor perturbation spectra generally acquire ξ-dependent corrections from the nonmetricity scalar Q. The manuscript does not explicitly derive or state the modified expressions for the slow-roll parameters ε, η or the power spectra (instead of the standard GR forms ns = 1 - 6ε + 2η, r = 16ε). This is load-bearing for the agreement claim; unaccounted corrections could alter the quoted values outside observational bounds.
  2. De Sitter inflation analysis: The viable interval 10^{-3} ≲ ξ ≲ 10^{-2} is obtained by requiring ns and r to lie inside Planck bounds, while the upper limit ξ < κ/(2p) with p=60 is presented as a model consistency constraint. The abstract links p directly to the choice N=60 used for the Cosh predictions, so it must be shown whether p (and thus the ξ bound) is fixed independently of the observational fitting or whether the parameter choices are selected post-hoc to produce agreement. This affects the robustness of the reported 'narrow allowed region'.
minor comments (2)
  1. Abstract: The LaTeX line break in the Cosh-type predictions (ns ≈ 0.965 - 0.967, r ≈ 0.017 - 0.018) should be removed for readability in the published version.
  2. General: Include at least one table or figure summarizing the ns and r values across the explored ξ and N ranges, with explicit comparison to Planck 2018 bounds, to make the agreement quantitative rather than qualitative.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address the major comments point by point below, providing clarifications on the derivations and parameter choices. We agree that additional explicit statements are warranted and will revise the manuscript accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: Abstract and Cosh-type model analysis: The central claim that the Cosh-type model yields ns ≈ 0.965-0.967 and r ≈ 0.017-0.018 at N=60 in excellent agreement with Planck data rests on the computation of these observables. In f(Q, φ) gravity with nonminimal ξ coupling, the background equations and scalar/tensor perturbation spectra generally acquire ξ-dependent corrections from the nonmetricity scalar Q. The manuscript does not explicitly derive or state the modified expressions for the slow-roll parameters ε, η or the power spectra (instead of the standard GR forms ns = 1 - 6ε + 2η, r = 16ε). This is load-bearing for the agreement claim; unaccounted corrections could alter the quoted values outside observational bounds.

    Authors: We thank the referee for highlighting this point. In Section 3 of the manuscript, the background equations and linear perturbations are derived from the action of f(Q,φ) gravity with the nonminimal coupling term. For the specific form f(Q,φ) = Q + ξ φ² Q (or equivalent), the ξ-dependent contributions to the curvature perturbation and tensor modes cancel at leading slow-roll order, yielding the standard expressions ns = 1 − 6ε + 2η and r = 16ε with ε and η computed from the effective potential. We acknowledge that these steps were not stated with sufficient explicitness. We will revise the text to include the full derivation of the perturbation spectra, the definitions of ε and η, and a demonstration that higher-order ξ corrections are negligible within the slow-roll regime, thereby justifying the quoted values for the Cosh model. revision: yes

  2. Referee: De Sitter inflation analysis: The viable interval 10^{-3} ≲ ξ ≲ 10^{-2} is obtained by requiring ns and r to lie inside Planck bounds, while the upper limit ξ < κ/(2p) with p=60 is presented as a model consistency constraint. The abstract links p directly to the choice N=60 used for the Cosh predictions, so it must be shown whether p (and thus the ξ bound) is fixed independently of the observational fitting or whether the parameter choices are selected post-hoc to produce agreement. This affects the robustness of the reported 'narrow allowed region'.

    Authors: The quantity p appearing in the bound ξ < κ/(2p) is the number of e-folds N. In the De Sitter analysis (Section 4), this bound follows directly from the requirement that the slow-roll conditions remain satisfied and the coupling stays perturbative for the entire inflationary phase; it is obtained prior to any comparison with data. The conventional choice N = 60 is adopted because it is the standard value needed to solve the horizon and flatness problems, as is common in the literature. The interval 10^{-3} ≲ ξ ≲ 10^{-2} is then the overlap between this theoretical upper limit and the region where ns and r fall inside Planck bounds. We will add an explicit paragraph clarifying the logical order of these steps and confirming that N = 60 is not chosen post-hoc to force agreement. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained

full rationale

The paper specifies explicit functional forms for f(Q,φ) including the nonminimal ξ coupling, adopts standard De Sitter and Cosh-type potentials, derives the modified Friedmann and perturbation equations, extracts slow-roll parameters ε and η, and evaluates ns(N,ξ) and r(N,ξ) from those. The quoted numerical values at N=60 and the restricted ξ interval are direct evaluations or observational constraints on the resulting expressions, not reductions of the outputs to the inputs by definition or by self-citation. Conventional choice of N≈60 and data-driven bounds on ξ do not constitute fitted-input-called-prediction or self-definitional circularity; the central claims retain independent content from the f(Q,φ) framework. No load-bearing self-citations or uniqueness theorems from prior author work are invoked.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

Central claims rest on coupling ξ whose range is fixed by data compatibility, conventional 60 e-folds, and standard slow-roll assumptions in FLRW cosmology; no new entities postulated.

free parameters (4)
  • ξ = 10^{-3} to 10^{-2}
    Coupling strength whose narrow interval is selected so ns and r fall inside Planck bounds.
  • N = 60
    Number of e-folds fixed at conventional value of 60 to obtain quoted predictions.
  • p = 60
    Exponent in derived upper bound ξ < κ/(2p).
  • κ = 1
    Normalization factor set to 1 in consistency bound.
axioms (2)
  • domain assumption Background is flat FLRW metric undergoing slow-roll inflation.
    Invoked to derive ns and r from modified gravity action.
  • domain assumption Nonminimal coupling takes form ξ φ² Q inside f(Q,φ).
    Assumed to obtain reported dependence on ξ.

pith-pipeline@v0.9.0 · 10744 in / 1564 out tokens · 127034 ms · 2026-05-07T14:56:46.454256+00:00 · methodology

0 comments
read the original abstract

In this work, we investigated several inflationary scenarios within the framework of modified $f(Q,\phi)$ gravity with a nonminimal coupling between the scalar field and the nonmetricity scalar. We focused on the impact of the coupling parameter $\xi$ on the inflationary observables, namely the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$. In the case of De Sitter inflation, we showed that the model can reproduce observationally viable predictions only within a restricted range of the coupling parameter. Specifically, we found that $n_s$ increases with $\xi$, while $r$ decreases, leading to a narrow allowed region $10^{-3} \lesssim \xi \lesssim 10^{-2}$ compatible with Planck data. Outside this range, the model either predicts excessively large tensor modes or an unphysical blue-tilted spectrum. We also derived theoretical constraints on $\xi$ from the consistency of the model, leading to an upper bound $\xi < \frac{\kappa}{2p}$. For $\kappa = 1$ and $p = 60$, this implies $\xi < 0.00833$, with a preferred region around $\xi \sim \mathcal{O}(10^{-3})$. Furthermore, we analyzed the Cosh-type inflationary model and showed that it provides a robust and consistent description of inflation. In this case, the tensor-to-scalar ratio decreases while the scalar spectral index increases with the number of e-folds $N$. For $N = 60$, the model predicts $n_s \approx 0.965 - 0.967, \qquad r \approx 0.017 - 0.018$, in excellent agreement with current observational constraints. Overall, our results highlight the crucial role of the nonminimal coupling in shaping the inflationary dynamics and ensuring compatibility with cosmological observations.

Figures

Figures reproduced from arXiv: 2604.26156 by F.K. Ahloui, F. Mavoa, M.B. Barry, M.G. Ganiou, R. Ndioukane.

Figure 1
Figure 1. Figure 1: Numerical evolution of the inflationary observables. Top panel: scalar spectral index view at source ↗
Figure 2
Figure 2. Figure 2: Tensor-to-scalar ratio r versus scalar spectral index ns for κ = 1, C1 = 10−6 , and H0 = 10−5 . 11 view at source ↗
Figure 3
Figure 3. Figure 3: Numerical evolution of the inflationary observables. Left panel: tensor-to-scalar ratio view at source ↗
Figure 4
Figure 4. Figure 4: Tensor-to-scalar ratio r as a function of the scalar spectral index ns for κ = 1, p = 60, and V0 = 1. 17 view at source ↗
Figure 5
Figure 5. Figure 5: Numerical evolution of the inflationary observables. Left panel: tensor-to-scalar ratio view at source ↗
Figure 6
Figure 6. Figure 6: Tensor-to-scalar ratio r as a function of the scalar spectral index ns. The parameters are fixed to ξ = 0.0083, γ = 1, κ = 1, and C4 = 1. 22 view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

43 extracted references · 43 canonical work pages

  1. [1]

    Observational evidence from supernovae for an accelerating universe and a cosmological constant,

    A. G. Riess et al., “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” Astron. J. 116 (1998) 1009–1038

    work page 1998

  2. [2]

    Measurements of Ω and Λ from 42 High Redshift Supernovae,

    S. Perlmutter et al., “Measurements of Ω and Λ from 42 High Redshift Supernovae,” Astrophys. J. 517 (1999) 565–586

    work page 1999

  3. [3]

    Type Ia supernova discoveries atz >1 from the Hubble Space Telescope,

    A. G. Riess et al., “Type Ia supernova discoveries atz >1 from the Hubble Space Telescope,” Astrophys. J. 607 (2004) 665–687

    work page 2004

  4. [4]

    Detection of the Baryon Acoustic Peak,

    D. J. Eisenstein et al., “Detection of the Baryon Acoustic Peak,” Astrophys. J. 633 (2005) 560–574

    work page 2005

  5. [5]

    Planck 2018 results. VI. Cosmological parameters,

    N. Aghanim et al. (Planck Collaboration), “Planck 2018 results. VI. Cosmological parameters,” Astron. Astrophys. 641 (2020) A6. 24

    work page 2018

  6. [6]

    The Cosmological Constant and Dark Energy,

    P. J. E. Peebles and B. Ratra, “The Cosmological Constant and Dark Energy,” Rev. Mod. Phys. 75 (2003) 559–606

    work page 2003

  7. [7]

    The Cosmological Constant Problem,

    S. Weinberg, “The Cosmological Constant Problem,” Rev. Mod. Phys. 61 (1989) 1–23

    work page 1989

  8. [8]

    f(R) Theories of Gravity,

    T. P. Sotiriou and V. Faraoni, “f(R) Theories of Gravity,” Rev. Mod. Phys. 82 (2010) 451–497

    work page 2010

  9. [9]

    Fujii and K

    Y. Fujii and K. Maeda, The scalar-tensor theory of gravitation, Cambridge University Press (2007)

    work page 2007

  10. [10]

    Modified Gauss-Bonnet theory as gravitational alternative for dark energy,

    S. Nojiri and S. D. Odintsov, “Modified Gauss-Bonnet theory as gravitational alternative for dark energy,” Phys. Lett. B 631 (2005) 1–6

    work page 2005

  11. [11]

    Renormalization of Higher Derivative Quantum Gravity,

    K. S. Stelle, “Renormalization of Higher Derivative Quantum Gravity,” Phys. Rev. D 16 (1977) 953–969

    work page 1977

  12. [12]

    Modified Gravity and Cosmology,

    T. Clifton et al., “Modified Gravity and Cosmology,” Phys. Rept. 513 (2012) 1–189

    work page 2012

  13. [13]

    Unified cosmic history in modified gravity,

    S. Nojiri and S. D. Odintsov, “Unified cosmic history in modified gravity,” Phys. Rept. 505 (2011) 59–144

    work page 2011

  14. [14]

    Symmetric teleparallel general relativity,

    J. M. Nester and H.-J. Yo, “Symmetric teleparallel general relativity,” Chin. J. Phys. 37 (1999) 113

    work page 1999

  15. [15]

    Coincident General Relativity,

    J. Beltr´ an Jim´ enez, L. Heisenberg, and T. Koivisto, “Coincident General Relativity,” Phys. Rev. D 98 (2018) 044048

    work page 2018

  16. [16]

    Cosmology inf(Q) geometry,

    J. Beltr´ an Jim´ enez et al., “Cosmology inf(Q) geometry,” Phys. Rev. D 101 (2020) 103507

    work page 2020

  17. [17]

    Review onf(Q) gravity,

    L. Heisenberg, “Review onf(Q) gravity,” Phys. Rept. 1066 (2024) 1–78

    work page 2024

  18. [18]

    Cosmological Dynamics on a Novelf(Q) Gravity Model with Recent DESI DR2 Observation,

    S. A. Kadam, D. Revanth Kumar, and S. K. Yadav, “Cosmological Dynamics on a Novelf(Q) Gravity Model with Recent DESI DR2 Observation,” arXiv:2601.06438

    work page arXiv

  19. [19]

    Inflationary universe: A possible solution to the horizon and flatness problems,

    A. H. Guth, “Inflationary universe: A possible solution to the horizon and flatness problems,” Phys. Rev. D 23 (1981) 347–356

    work page 1981

  20. [20]

    A new inflationary universe scenario,

    A. D. Linde, “A new inflationary universe scenario,” Phys. Lett. B 108 (1982) 389–393

    work page 1982

  21. [21]

    Quantum fluctuations and a nonsingular universe,

    V. F. Mukhanov and G. V. Chibisov, “Quantum fluctuations and a nonsingular universe,” JETP Lett. 33 (1981) 532–535

    work page 1981

  22. [22]

    Theory of cosmological perturba- tions,

    V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, “Theory of cosmological perturba- tions,” Phys. Rept. 215 (1992) 203–333

    work page 1992

  23. [23]

    Planck 2018 results. VI. Cosmological parameters,

    N. Aghanim et al. (Planck Collaboration), “Planck 2018 results. VI. Cosmological parameters,” Astron. Astrophys. 641 (2020) A6

    work page 2018

  24. [24]

    Planck 2018 results. X. Constraints on inflation,

    Planck Collaboration, “Planck 2018 results. X. Constraints on inflation,” Astron. Astrophys. 641 (2020) A10. 25

    work page 2018

  25. [25]

    Chaotic Inflation,

    A. D. Linde, “Chaotic Inflation,” Phys. Lett. B129, 177 (1983)

    work page 1983

  26. [26]

    Cosmological Inflation and Large-Scale Structure,

    A. R. Liddle and D. H. Lyth, “Cosmological Inflation and Large-Scale Structure,” Cambridge University Press (2000)

    work page 2000

  27. [27]

    A New Type of Isotropic Cosmological Models Without Singularity,

    A. A. Starobinsky, “A New Type of Isotropic Cosmological Models Without Singularity,” Phys. Lett. B91, 99 (1980)

    work page 1980

  28. [28]

    f(R) theories,

    A. De Felice and S. Tsujikawa, “f(R) theories,” Living Rev. Relativity13, 3 (2010)

    work page 2010

  29. [29]

    Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models,

    S. Nojiri and S. D. Odintsov, “Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models,” Phys. Rept.505, 59 (2011)

    work page 2011

  30. [30]

    f(T) teleparallel gravity and cosmology,

    Y.-F. Cai, S. Capozziello, M. De Laurentis, and E. N. Saridakis, “f(T) teleparallel gravity and cosmology,” Rept. Prog. Phys.79, 106901 (2016)

    work page 2016

  31. [31]

    Modified teleparallel theories of gravity,

    S. Bahamonde, C. G. B¨ ohmer, and M. Wright, “Modified teleparallel theories of gravity,” Phys. Rev. D92, 104042 (2015)

    work page 2015

  32. [32]

    f(R,T) gravity,

    T. Harko, F. S. N. Lobo, S. Nojiri, and S. D. Odintsov, “f(R,T) gravity,” Phys. Rev. D84, 024020 (2011)

    work page 2011

  33. [33]

    Accelerating universe from f(R,T) gravity,

    R. Myrzakulov, “Accelerating universe from f(R,T) gravity,” Eur. Phys. J. C72, 2203 (2012)

    work page 2012

  34. [34]

    Teleparallel Palatini theories,

    J. B. Jim´ enez, L. Heisenberg and T. Koivisto, “Teleparallel Palatini theories,” Phys. Rev. D98, 044048 (2018)

    work page 2018

  35. [35]

    Observational constraints off(Q) gravity,

    R. Lazkoz, F. S. N. Lobo, M. Ortiz-Ba˜ nos and V. Salzano, “Observational constraints off(Q) gravity,” Phys. Rev. D100, 104027 (2019)

    work page 2019

  36. [36]

    Inflationary models in modified gravity,

    Z. Haba, A. Stachowski, and M. Szydlowski, “Inflationary models in modified gravity,”Eur. Phys. J. C75, 2550049 (2015)

    work page 2015

  37. [37]

    Inflationary Cosmology after Planck 2013

    A. Linde, “Inflationary Cosmology after Planck 2013,” arXiv:1402.0526v2 [hep-th]

    work page Pith review arXiv 2013

  38. [38]

    S. D. Odintsov, V. K. Oikonomou, I. Giannakoudi, F. P. Fronimos and E. C. Lymperiadou, arXiv:2307.16308 [gr-qc]

    work page arXiv

  39. [39]

    Goheer, R

    N. Goheer, R. Goswami, J. Larena, P. K. S. Dunsby and K. Ananda, AIP Conf. Proc.1241 (2009) 898, doi:10.1063/1.3462731

    work page doi:10.1063/1.3462731 2009

  40. [40]

    A. R. Liddle and D. H. Lyth,Cosmological Inflation and Large-Scale Structure, Cambridge Uni- versity Press, Cambridge, UK (2000)

    work page 2000

  41. [41]

    E. J. Copeland, A. R. Liddle, and D. Wands, Exponential potentials and cosmological scaling solutions,Phys. Rev. D57, 4686 (1998)

    work page 1998

  42. [42]

    Tsujikawa, Quintessence: a review,Class

    S. Tsujikawa, Quintessence: a review,Class. Quantum Grav.30, 214003 (2013)

    work page 2013

  43. [43]

    Habaet al.,International Journal of Modern Physics D, Vol

    S. Habaet al.,International Journal of Modern Physics D, Vol. 34, No. 12 (2025) 2550049. 26

    work page 2025