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arxiv: 2605.22309 · v1 · pith:OS3SCH6Enew · submitted 2026-05-21 · 🌌 astro-ph.CO · gr-qc· hep-ph

Signatures of Modified Gravity Below mathcal{O}(10) Mpc in a Dynamical Dark Energy Background

Yo Toda , Adri\`a G\'omez-Valent This is my paper

Pith reviewed 2026-05-22 05:32 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-ph
keywords modified gravitydynamical dark energystructure growthcosmological constraintsredshift space distortionsCMB constraints
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The pith

Modified gravity must act below roughly 10 megaparsecs to reconcile dynamical dark energy with structure growth observations.

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

The paper examines whether a dynamical dark energy model can fit cosmological data better when combined with modifications to gravity on small scales. It parametrizes changes to the effective strength of gravity below a cutoff scale in two redshift ranges. The analysis shows that to reduce the predicted clustering of galaxies at low redshifts without clashing with cosmic microwave background measurements, these gravity changes have to start at scales around 10 Mpc or smaller. Including these effects improves the fit for the dynamical dark energy parameters compared to standard gravity. This points to a specific regime where deviations from general relativity could be tested.

Core claim

In a universe with dynamical dark energy described by the CPL parametrization, any departure of the effective gravitational coupling from Newton's constant must occur sharply below a comoving scale of order 10 Mpc to suppress structure growth at low redshifts while remaining consistent with CMB constraints from the late-time integrated Sachs-Wolfe effect and lensing.

What carries the argument

A two-bin parametrization of the effective gravitational coupling that differs from Newton's constant below a single comoving scale lambda_c, held constant within each redshift bin from z=0 to 1 and z=1 to 3.

Load-bearing premise

The model assumes that any change in the effective gravitational strength happens abruptly below one fixed scale and stays constant across each broad redshift interval without varying inside those intervals.

What would settle it

A precise measurement of the growth rate of structure or the effective gravitational coupling on scales around 10 Mpc at redshifts below 1 that shows no deviation from general relativity would contradict the necessity of the modified gravity component.

Figures

Figures reproduced from arXiv: 2605.22309 by Adri\`a G\'omez-Valent, Yo Toda.

Figure 3
Figure 3. Figure 3: FIG. 3. Triangle plots (at 68% and 95% CL) for the models [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Triangle plots (at 68% and 95% CL) for the CPL [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
read the original abstract

Cosmological data from the cosmic microwave background (CMB), baryon acoustic oscillations, and Type Ia supernovae suggest that the component driving the accelerated expansion of the Universe may be dynamical at the $\sim 2.5$-$3\sigma$ CL. The best-fit CPL model produces a level of cosmic structure similar to that of $\Lambda$CDM, with both models exhibiting mild tension with redshift-space distortion data. In this {\it Letter}, we parametrize possible departures of the effective gravitational coupling from Newton's constant in the late Universe, below a comoving scale $\lambda_c$, using two redshift bins, $0 \leq z < 1$ and $1 \leq z \leq 3$. We then determine the optimal values of $\lambda_c$ and the amplitude of these deviations from General Relativity, assuming a background with dynamical dark energy in CPL form. We find that, in order to achieve the required suppression of structure growth at low redshifts while remaining consistent with CMB constraints -- primarily from the late-time ISW effect at low $\ell$ and lensing at high $\ell$ -- modified gravity effects must appear on scales smaller than $\lambda_c \sim \mathcal{O}(10)\,\mathrm{Mpc}$. Using Planck PR4, DESI DR2, Pantheon+ (or DES-Dovekie) and redshift-space distortions data we confirm that a CPL background with standard gravity is moderately preferred over $\Lambda$CDM; this preference strengthens to a mildly strong level when modified gravity effects are included. This enhancement leaves the CPL parameters largely unchanged, but shifts them slightly further into the quintom region.

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

1 major / 2 minor

Summary. The manuscript parametrizes departures of the effective gravitational coupling from Newton's constant below a single comoving scale lambda_c, with constant amplitude in each of two fixed redshift bins (0 <= z < 1 and 1 <= z <= 3), on a CPL dynamical dark energy background. Fits to Planck PR4, DESI DR2, Pantheon+ (or DES-Dovekie) and RSD data are reported to yield lambda_c ~ O(10) Mpc as the scale required to suppress low-redshift structure growth sufficiently to match RSD while remaining consistent with CMB constraints from the late-time ISW effect at low ell and lensing at high ell. The inclusion of these modified-gravity effects is stated to strengthen the preference for CPL over LambdaCDM, with CPL parameters largely unchanged but shifted slightly further into the quintom region.

Significance. If the modeling assumptions are robust, the result would identify a concrete scale below which modified gravity could reconcile the mild RSD tension with standard models without spoiling CMB consistency, while modestly enhancing the dynamical dark energy preference. The use of multiple recent datasets (Planck PR4, DESI DR2, Pantheon+) provides a broad observational basis, but the significance is limited by the lack of tests against alternative scale dependences.

major comments (1)
  1. [two-bin parametrization paragraph] The paragraph introducing the two-bin parametrization states that the effective gravitational coupling is exactly 1 above lambda_c and takes a constant offset below it, separately in each redshift bin, with no k-dependence inside the bins. This modeling choice is load-bearing for the central claim that lambda_c must be O(10) Mpc: a smoother transition (e.g., tanh roll-off) or additional scale dependence within bins could achieve the same integrated RSD suppression with a larger effective cutoff while still satisfying the same CMB ISW and lensing constraints, weakening the necessity of the reported scale.
minor comments (2)
  1. [Abstract] Clarify which supernova dataset (Pantheon+ or DES-Dovekie) is used for the primary chains versus the alternative; the abstract presents both without indicating the baseline choice.
  2. [Data and likelihood section] The covariance treatment between RSD and DESI BAO measurements should be stated explicitly, including whether any cross-covariance is included or neglected.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We respond to the major comment below and have revised the text to clarify the modeling assumptions and their implications for the reported scale.

read point-by-point responses

  1. Referee: [two-bin parametrization paragraph] The paragraph introducing the two-bin parametrization states that the effective gravitational coupling is exactly 1 above lambda_c and takes a constant offset below it, separately in each redshift bin, with no k-dependence inside the bins. This modeling choice is load-bearing for the central claim that lambda_c must be O(10) Mpc: a smoother transition (e.g., tanh roll-off) or additional scale dependence within bins could achieve the same integrated RSD suppression with a larger effective cutoff while still satisfying the same CMB ISW and lensing constraints, weakening the necessity of the reported scale.

    Authors: We agree that the sharp cutoff with constant amplitude below lambda_c and no additional k-dependence within bins is a deliberate simplifying choice in our parametrization. This approach was adopted to isolate the characteristic comoving scale at which modifications become necessary while remaining computationally efficient for the MCMC analysis. We acknowledge that a smoother transition (such as a tanh roll-off) or intra-bin scale dependence could in principle redistribute the suppression and permit a modestly larger effective cutoff while preserving consistency with the ISW and lensing constraints. Nevertheless, within the adopted framework the data still require that the onset of modifications occur on scales of order 10 Mpc to achieve the observed RSD suppression without over-affecting the CMB. We have added a new paragraph in Section 3 of the revised manuscript explicitly discussing this modeling limitation, noting that the quoted scale is specific to the step-like parametrization, and highlighting the value of exploring continuous scale dependences in future work. revision: partial

standing simulated objections not resolved
  • Quantitative assessment of the shift in preferred lambda_c under a smoother transition function (e.g., tanh) has not been performed and would require new model implementations and additional sampling runs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on a phenomenological parametrization of scale-dependent gravity modifications whose amplitude and cutoff are fitted directly to the same data used to evaluate consistency; no independent evidence for the functional form is supplied.

free parameters (2)
  • lambda_c
    Comoving scale below which effective gravitational coupling deviates from Newton's constant; fitted to achieve required structure-growth suppression.
  • deviation_amplitudes
    Two independent amplitudes (one per redshift bin) that quantify the departure from GR; fitted jointly with lambda_c.
axioms (2)
  • domain assumption The background expansion follows the CPL parametrization of dynamical dark energy.
    Invoked when stating that the model assumes a CPL background while adding MG effects.
  • domain assumption CMB constraints on the model are dominated by the late-time ISW effect at low multipoles and lensing at high multipoles.
    Used to argue that the chosen MG scale remains consistent with Planck data.
invented entities (1)
  • scale-dependent effective gravitational coupling below lambda_c no independent evidence
    purpose: To suppress structure growth at low redshifts while preserving CMB consistency.
    New phenomenological entity introduced to parametrize departures from GR; no independent falsifiable prediction outside the fit is provided.

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