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This paper reconstructs the f(Q) modified-gravity action directly from DESI DR2 BAO and DESyr5 supernova data and finds that the gravitational-wave amplitude damping parameter at z=0, ν = 0.18 +0.08/−0.07, deviates from general relativity's

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Reconstructing the dark energy density from DESI BAO and DESyr5 supernovae, then recasting it as f(Q) gravity, predicts a low-redshift gravitational wave damping ν≈0.18 (≳2σ from GR) only for the DESyr5 dataset.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection The DESI+DESyr5-based f(Q) reconstruction gives a striking ν≈0.18 GW damping forecast at z=0, but the result is dataset- and boundary-condition-dependent; still a useful benchmark worth peer review. the 4 major comments →

arxiv 2509.07976 v1 pith:52OIKVPH submitted 2025-09-09 gr-qc astro-ph.CO

Dynamical Dark Energy or Modified Gravity? Signatures in Gravitational Wave Propagation

Purnendu Karmakar , Sandeep Haridasu This is my paper
classification gr-qc astro-ph.CO
keywords f(Q) gravitymodified gravitygravitational wave dampingdynamical dark energyDESI BAO DR2DESyr5 supernovaeeffective gravitational couplingnon-metricity gravity
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.

The reading

The paper claims that the recent hints of dynamical dark energy in the DESI DR2 BAO and DESyr5 supernova data, when read through the non-metricity-based f(Q) theory of modified gravity, turn into a concrete prediction for gravitational-wave astronomy: an amplitude damping parameter ν = 0.18 +0.08/−0.07 at z = 0, more than 2σ away from general relativity's ν = 0. The authors get there without assuming any functional form for the modified-gravity action — they fit the dark-energy density as a cubic polynomial in the scale factor and reconstruct the f(Q) Lagrangian from it. The scalar-sector signature, the effective gravitational coupling μ, stays almost unchanged (about 2% above Newton's constant) and is identical for both supernova samples, so structure growth cannot separate modified gravity from dark energy; only the gravitational-wave channel can. The result is dataset-dependent — the older Pantheon+ sample keeps ν consistent with zero — which makes supernova systematics the deciding factor. If the claim holds, LISA, Einstein Telescope, and Cosmic Explorer should see gravitational waves damped substantially more at low redshift than general relativity allows.

Core claim

A cubic-Taylor fit of the dark-energy density to DESI DR2 BAO plus DESyr5 supernovae, fed through the ODE F = 6H²(Ωde + 2F_Q) with gauge Q = 6H² and boundary condition F_Q → 0 at z = 5, yields a reconstructed f(Q) Lagrangian with no assumed functional form. From it, the effective gravitational coupling μ = 1/(1+F_Q) stays near unity (≈2% enhancement at z=0, dataset-independent), while the gravitational-wave damping parameter ν = 12ḢF_QQ/(1+F_Q) rises steeply at low redshift to 0.18 +0.08/−0.07 at z=0 for DESI+DESyr5 — a ≳2σ departure from GR's ν=0. With Pantheon+, ν stays consistent with zero, so the tensor signature is specific to the DESyr5 sample. The reconstructed F(z) matches a cosmolog

What carries the argument

The load-bearing object is the reconstructed F(Q) — the non-linear part of the f(Q) action — obtained by solving the first-order ODE F = 6H²(Ωde + 2F_Q) with gauge Q = 6H² and boundary condition F_Q → 0 at z = 5, with the dark-energy density input as a cubic Taylor expansion in the scale factor whose coefficients are fit to data. The ODE is the bridge from the background to perturbations: F, F_Q and F_QQ feed the scalar signature μ = 1/(1+F_Q) (the quasi-static effective gravitational coupling) and the tensor signature ν = 12ḢF_QQ/(1+F_Q) (gravitational-wave amplitude damping). Because μ and ν are derived, not fitted, any deviation from GR is a direct consequence of the reconstructed Lagrang

Load-bearing premise

The reconstruction assumes, without a physical argument, that the derivative of the modified-gravity function vanishes at redshift 5 and that a third-order Taylor expansion of the dark-energy density is accurate over the fitted range; change either assumption and the >2σ gravitational-wave damping signal changes (the alternative boundary condition makes it larger), so the detection significance is hostage to two unstated conventions.

What would settle it

Direct standard-siren tests: with tens of binary-neutron-star events, Einstein Telescope and Cosmic Explorer can measure ν(z) from the mismatch between gravitational-wave and electromagnetic distances. If the low-z damping is found consistent with GR (ν = 0) at better than 2σ, the DESyr5-based reconstruction is falsified. Nearer term, re-running the same pipeline with a fourth-order Taylor expansion, or with the alternative boundary condition F → 0 anchored at different redshifts, shows whether the >2σ signal survives; if it drops below 2σ, the deviation is a truncation or boundary artifact.

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

If this is right

  • If ν ≈ 0.18 at z = 0 is correct, next-generation gravitational-wave observatories (LISA, Einstein Telescope, Cosmic Explorer) should measure stronger-than-GR damping of gravitational-wave amplitudes at low redshift — a direct, testable target for standard-siren cosmology.
  • Because Pantheon+ and DESyr5 give different ν reconstructions (zero versus 0.18), the choice of supernova compilation decides whether modified gravity is favoured; settling the systematics between these samples is a precondition for any detection claim.
  • The reconstructed ν changes sign with redshift, ruling out the large class of parametric f(Q) models that predict a single-sign damping throughout cosmic history; future tensor-sector data can therefore prune the model space.
  • The effective gravitational coupling μ remaining near unity (≈1.01–1.02 at z=0) means structure-growth measurements cannot easily distinguish f(Q) gravity from ΛCDM; the discriminator has to come from the gravitational-wave channel.
  • The reconstructed F(z) is consistent with f(Q) = Q + Λ at high redshift, with deviations confined to z ≲ 1.5 — tying the modified-gravity signature directly to the redshift range where DESI and supernova data hint at dynamical dark energy.

Where Pith is reading between the lines

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

  • Editor's inference: the >2σ ν signal is partly a function of the boundary choice — Approach-I (F → 0 at high z) would give larger deviations, and the paper offers no physical reason to prefer the F_Q → 0 condition; the true significance is prior-dependent and should be re-derived under both approaches with marginalization over the boundary redshift.
  • Editor's inference: the third-order Taylor truncation of the dark-energy density is a second silent choice; repeating the reconstruction at fourth order or with a regularized (e.g., Padé) expansion would reveal whether the steep low-z rise in ν is physical or a truncation artifact.
  • Editor's inference: the sign-changing ν(z) is a fingerprint that could distinguish non-metricity gravity from other modified-gravity families — curvature-based theories like f(R) modify the GW friction term differently — so measuring ν(z) with future standard sirens could identify the theory class, not merely separate modified gravity from dark energy.
  • Editor's inference: the same background-to-perturbation pipeline — fit the density, solve the reconstruction ODE, derive μ and ν — can be applied to other geometric reformulations such as f(T) or f(P), giving each class a characteristic prediction to compare against the same datasets.
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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

4 major / 6 minor

Summary. The paper reconstructs the dark energy density from DESI DR2 BAO plus one of two SNe compilations (Pantheon+ or DESyr5) using a cubic Taylor expansion in the scale factor. It then translates this background reconstruction into the f(Q) modified-gravity function by solving Eq. (27) under the coordinate choice Q=6H² and an assumed boundary condition, and computes the effective gravitational coupling μ and the GW amplitude-damping parameter ν. The headline result is that DESI+DESyr5 yields ν=0.18+0.08−0.07 at z=0, a >2σ departure from the GR value ν=0, while DESI+Pan+ yields ν=0±0.06. The authors argue that this provides a target for next-generation GW detectors to distinguish f(Q) gravity from dark energy within GR.

Significance. If the reconstruction were robust, the paper would be a valuable demonstration that current background data, interpreted within f(Q) gravity, produce a specific, testable prediction for GW amplitude damping that differs between SNe datasets. The methodology of parameterizing the DE density rather than a specific f(Q) form is useful and extendable to other modified-gravity theories. However, the headline ν signal is conditional on the chosen dataset and on an arbitrary boundary condition in the reconstruction; it is not a direct measurement of GW damping. The reported credible intervals omit the dominant systematic uncertainties. The paper's main value is as a framework and forecast, not as evidence for modified gravity.

major comments (4)
  1. [III, Eq. (27); V.1] The reconstructed ν is not robust to the boundary condition used to integrate Eq. (27). This is a first-order linear ODE, so for a given background solution the homogeneous mode is fixed only by the initial condition. The choice F_Q→0 at z=5 (Approach-II) is an input, not a datum; ν in Eq. (25) depends on F_QQ and F_Q and therefore inherits this choice. The paper itself states that Approach-I produces 'slightly larger deviations' but gives no physical or observational criterion for preferring Approach-II. The quoted 68% credible interval for ν therefore marginalizes only over the background Taylor coefficients and cosmological parameters, not over the boundary-condition ambiguity. The '≳2σ deviation' is thus a statement about a specific reconstruction convention, not a robust data-driven prediction.
  2. [V.1; Abstract] The central claim is strongly dataset-dependent: DESI+Pan+ gives ν=0±0.06, consistent with GR, while DESI+DESyr5 gives ν=0.18±0.08. The paper attributes this to 'different systematics' in the SNe compilations without quantifying that assessment or showing a model-comparison. Since the abstract claims a 'significant distinct signature' and the conclusions present the DESyr5 result as a 'strong case' for GW tests, the authors should either provide a formal systematic-error treatment or explicitly frame the DESyr5 result as conditional on that dataset and not a robust finding.
  3. [III, Eq. (26)] The cubic Taylor expansion of ρ_de(a) is assumed to converge over the full data range without a demonstrated convergence test. The reconstructed μ and ν involve derivatives of the fitted F(Q), so truncation errors are amplified. The validation cited—agreement of the derived w_de with a previous analysis—is insufficient for derivative quantities. A robustness check with a fourth-order term, a different basis, or a binned reconstruction should be provided to verify that the ν signal is not an artifact of the truncation.
  4. [III; V.1] The paper repeatedly calls the reconstruction 'model-independent', but the signatures are derived under several assumptions: f(Q) gravity, the coordinate choice Q=6H², the Taylor parameterization of ρ_de, and the boundary condition for Eq. (27). The abstract should be clearer that μ and ν are theoretical translations of the background fit under these assumptions, not independent observables. This would prevent readers from interpreting the 2σ deviation as a measurement of GW damping.
minor comments (6)
  1. [V.1] Inconsistent numbers for ν at z=0: the text first says 'ν∼0.15 at z=0' and then reports 'ν=0.18+0.08−0.07 at 68% C.L.' The final constraint should be used consistently.
  2. [I] The Introduction states 'torsion called f(T) model, and non-metricity, called f(T).' The last f(T) should be f(Q).
  3. [Abstract and III] Grammar: 'We reconstruct of dark energy density' should be 'We reconstruct the dark energy density'.
  4. [V.1 (footnote)] The second footnote in Section V.1 is garbled and appears to be an incomplete note to the authors. It should be removed or rewritten as a proper sentence.
  5. [III] The claim that z=5 is 'well outside the range of observational data' is imprecise, since DESI DR2 BAO extends to z=4.2; z=5 is only slightly beyond the data.
  6. [II.2.1 and IV] The symbol μ is used for both the effective gravitational coupling (Eqs. 20–21) and the distance modulus in the SNe likelihood (Section IV). Use e.g. μ_eff for the coupling to avoid confusion.

Circularity Check

1 steps flagged

The reported ν>2σ GW-damping signal is a re-expression of the fitted dark-energy density, not an independent perturbation-level measurement, and depends on an un-marginalized reconstruction convention.

specific steps
  1. fitted input called prediction [Section III (Eqs. 26-27) and Section V.1 (Eq. 25)]
    "Once the dark energy density is obtained through the Bayesian inference, we then translate the dark energy density to the F(Q) function, solving the first order ordinary differential equation following Eq. (11), F(Q) = 6H^2 (Ωde + 2F_Q(Q)) ... Finally, we reconstruct the damping parameter ν from the reconstructed F_Q and F_QQ functions using Eq. (25) ... We find a constraint of ν = 0.18 +0.08 −0.07 at 68% C.L., which is a ≳2σ deviation from the GR scenario, ν = 0."

    Eq. (25) defines ν = 12 Hdot F_QQ/(1+F_Q), and F_Q and F_QQ are not measured but obtained by numerically solving Eq. (27) using the Ωde(z) fitted to SNe+BAO data through Eq. (26). The posterior of ν is therefore the transformed posterior of the fitted Taylor coefficients α_i and background parameters, together with the chosen initial condition; no tensor-mode, growth, or gravitational-wave data enter the reconstruction at any point. The claimed '>2σ deviation from GR' thus carries exactly the same information as the fitted dark-energy density deviating from a constant: it is a re-expression of the background fit by the paper's own equations, not an independent perturbation-level constraint.

full rationale

The central derived quantities μ and ν are computed from the background reconstruction, not measured independently. The paper fits ρ_de(z) via a third-order Taylor expansion and then solves the first-order ODE F(Q)=6H^2(Ωde+2F_Q) for each posterior sample; μ and ν follow algebraically from F_Q and F_QQ. This is a legitimate theoretical mapping, but the paper presents the resulting ν as a 'constraint' with a >2σ deviation from GR. By the paper's own equations, ν is statistically forced by the fitted background and the chosen boundary condition, so this matches the fitted-input-called-prediction pattern. The quoted interval also does not marginalize over the Approach-I vs Approach-II choice; the paper itself states that Approach-I yields 'slightly larger deviations' and that the initial condition is set at z=5 'well outside the range of observational data,' so the headline signal is partly convention-dependent. There is a minor self-citation for methodology ([34,68]), but it is not load-bearing: the paper states all relevant equations, and the datasets are external. No other circular steps were found; the derivation is otherwise self-contained, and the boundary-condition sensitivity, while important for robustness, is not itself a tautology.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The central derived quantities μ and ν depend on three fitted expansion coefficients (α1-α3), the fitted matter density, and a supernova absolute-magnitude nuisance parameter, together with several domain assumptions (flatness, quasi-static approximation, Q=6H² gauge) and two ad hoc choices: the Taylor truncation order and the initial condition for the ODE that defines f(Q). No new particles or fields are introduced.

free parameters (3)
  • α1, α2, α3 = not quoted in text
    Coefficients of the 3rd-order Taylor expansion of the dark energy density ratio Rde(a) (Eq. 26); fitted to SNe+BAO+IDL likelihood.
  • Ωm0 = not quoted
    Present-day matter density parameter; free parameter in the fit, with Ωde0 fixed by closure.
  • M_b (SNe absolute magnitude) = not quoted
    Nuisance parameter for Pantheon+; analytically marginalized for DESyr5.
axioms (5)
  • domain assumption Symmetric teleparallel f(Q) gravity with coordinate choice Q=6H²
    The reconstruction applies only to this branch of f(Q) theories; other connection choices give different predictions (Section II).
  • domain assumption Spatial flatness
    Assumed in the Friedmann equations and the luminosity distance formula (Section II.1).
  • domain assumption Quasi-static approximation for the effective gravitational coupling
    μ=1/f_Q is derived under sub-horizon quasi-static conditions (Section II.2.1).
  • ad hoc to paper 3rd-order Taylor expansion of Rde converges over the data redshift range a≤0.33 (z≥2)
    The authors state this convergence is 'validated' by agreement with [67] rather than proven (Section III, footnote).
  • ad hoc to paper Boundary condition F_Q→0 at z=5 (Approach-II)
    The ODE for F(Q) requires an initial condition; the chosen one gives Λ-like behavior at high z, and the authors note Approach-I gives different results (Section III).

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Dynamical Dark Energy or Modified Gravity? Signatures in Gravitational Wave Propagation." pith.science (2026). https://pith.science/paper/52OIKVPH

@misc{pith2026250907976,
  author       = {Pith},
  title        = {Pith review of: Dynamical Dark Energy or Modified Gravity? Signatures in Gravitational Wave Propagation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/52OIKVPH}},
  note         = {Machine review of arXiv:2509.07976}
}
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read the original abstract

We discuss the implications of the most recent DESI Baryon Acoustic Oscillations (BAO) DR2 and DESyr5 compilation of supernovae (SNe) datasets for modified gravity focusing on non-metricity based $f(Q)$ theory, by employing a `model-independent' approach. We reconstruct of dark energy density which is then extended to estimate the perturbation-level quantities, sourced by the modified gravity, namely the effective gravitational coupling, $\mu$, and the amplitude damping parameter of gravitational wave propagation, $\nu$. In light of the remarkable hints for a dynamical dark energy emerging from the analysis of background cosmological data, we discuss the possibility to distinguish between dark energy and modified gravity scenarios from their scalar and tensor perturbation-level signatures. We contrast our findings between the older Pantheon+ and the newer DESyr5 compilations of SNe datasets, which predict a significant distinct signature in the damping parameter of the gravitational wave propagation amplitude. On the other hand, the prediction for the effective gravitational coupling remains insensitive to the choice of the SNe datasets. Our results provide a strong case for the study of gravitational wave propagation in modified gravity theories, in light of the new generation of gravitational wave detectors such as LISA, Einstein Telescope and Cosmic Explorer.

Figures

Figures reproduced from arXiv: 2509.07976 by Purnendu Karmakar, Sandeep Haridasu.

Figure 1
Figure 1. Figure 1: FIG. 1. Posterior distributions of the dark energy density ( [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

discussion (0)

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.