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arxiv: 2606.10597 · v1 · pith:XPB2OGM2new · submitted 2026-06-09 · 🌌 astro-ph.CO

Synergy between the gravitational potential decay rate and other structure growth probes in testing gravity

Shang Li , Pengjie Zhang , Fuyu Dong This is my paper

Pith reviewed 2026-06-27 12:25 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords modified gravitygravitational potential decay ratestructure growthcosmological constraintsparameter estimationeffective field theoryphenomenological models
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The pith

Combining gravitational potential decay rate measurements with structure growth probes tightens constraints on modified gravity parameters by up to a factor of two.

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

The paper demonstrates that the gravitational potential decay rate responds to modified gravity parameters along degeneracy directions different from those of structure amplitude and growth rate measurements. Adding tomographic decay rate data to existing Σ8 constraints from CMB lensing and fσ8 measurements from galaxy surveys produces narrower bounds on the deviation parameters in both phenomenological and effective field theory descriptions. A reader would care because the combination tests whether gravity deviates from general relativity on large scales more decisively than any probe alone. The reported improvements reach a factor of roughly two for some parameters and 1.5 for others.

Core claim

Tomographic measurements of the gravitational potential decay rate, when added to CMB-lensing-tomography Σ8 and DESI fσ8 data, yield μ0 = 0.09 ± 0.35 and Σ0 = 0.01 ± 0.06 in the phenomenological parameterization where each modified gravity function scales with dark energy density; the Σ0 uncertainty shrinks by a factor of about two relative to Σ8 + fσ8 alone. For the (μ0, η0) pair the constraints improve by a factor of about 1.5. In the EFT α-basis with αi scaling with dark energy density, the parameters cM and cB have uncertainties roughly twice smaller than those from prior combinations that omitted the decay rate.

What carries the argument

The gravitational potential decay rate (DR), whose response to modified gravity parameters points in directions orthogonal to those of Σ8 and fσ8, allowing the joint data vector to break degeneracies.

If this is right

  • Σ0 constraints tighten by a factor of ~2 when decay rate data are included.
  • μ0 and η0 constraints each tighten by a factor of ~1.5.
  • EFT parameters cM and cB have uncertainties ~2 times smaller than those obtained without the decay rate measurements.

Where Pith is reading between the lines

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

  • Future analyses could test whether adding decay rate data also reduces tension between different cosmological datasets.
  • The same complementarity might appear when decay rate measurements are combined with weak lensing or redshift-space distortion measurements from other surveys.
  • Direct validation of the statistical independence assumption between decay rate and growth-rate vectors would strengthen or weaken the reported gains.

Load-bearing premise

The reported decay rate measurements share no significant unaccounted cross-covariance or common systematics with the Σ8 and fσ8 data vectors.

What would settle it

A joint covariance matrix computed between the decay rate data vector and the Σ8 + fσ8 vector that reveals large off-diagonal correlations would remove the claimed improvement in parameter precision.

read the original abstract

We test gravity by exploiting the synergy between the gravitational potential decay rate ($\mathit{DR}$) and complementary structure-growth probes: these observables respond to MG parameters with different degeneracy directions, so their combination yields stronger constraints than any single probe. We adopt the tomographic $\mathit{DR}$ measurements reported in \citep{2025ApJ...982...99D} and combine them with CMB-lensing-tomography $\Sigma_8$ constraints and $f\sigma_8$ measurements from DESI DR1 full-shape analyses and the DESI peculiar-velocity field. We apply this joint data vector to two representative frameworks: phenomenological parameterizations and the Effective Field Theory (EFT) $\alpha$-basis. For the phenomenological form $P_{\rm MG}(a)=1+P_{{\rm MG},0}\,\Omega_{\rm DE}(a)/\Omega_{\rm DE}(0)$, where $P_{\rm MG}$ denotes $\mu$, $\eta$, or $\Sigma$, we obtain $\mu_0=0.09\pm0.35$ and $\Sigma_0=0.01\pm0.06$. Compared to the measurements combination $\Sigma_8+f\sigma_8$, including $\mathit{DR}$ tightens the constraint on $\Sigma_0$ by a factor of $\sim2$. For the $(\mu_0,\eta_0)$ case we find $\mu_0=0.06^{+0.17}_{-0.23}$ and $\eta_0=-0.03^{+0.36}_{-0.46}$; relative to $\Sigma_8+f\sigma_8$, adding $\mathit{DR}$ improves the constraints on both parameters by a factor of $\sim1.5$. In the EFT $\alpha$-basis, adopting the parameterization $\alpha_i(a)=c_i\,\Omega_{\rm DE}(a)$ with $i\in\{{\rm M,B}\}$, we find $c_{\rm M}=0.64^{+0.32}_{-0.72}$ and $c{\rm B}=0.31^{+0.19}_{-0.29}$. The corresponding EFT uncertainties are about a factor of $\sim2$ smaller than those reported in \citep{2025JCAP...09..053I}, which combined DESI full-shape and BAO measurements with DES-SN5YR and CMB data. These results demonstrate the capability of $\mathit{DR}$ and the necessity of including the $\mathit{DR}$ measurements in testing gravity.

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 / 0 minor

Summary. The manuscript claims that tomographic DR measurements, when combined with CMB-lensing Σ8 and DESI fσ8 data, exploit differing degeneracy directions in modified gravity to yield tighter constraints than Σ8+fσ8 alone: Σ0 tightens by a factor of ~2, (μ0,η0) by ~1.5, and EFT α-basis uncertainties shrink by ~2 relative to a prior DESI+SN+CMB analysis.

Significance. If the joint analysis is robust, the work illustrates the value of DR as an independent growth probe with orthogonal sensitivity, strengthening tests of gravity in both phenomenological and EFT frameworks.

major comments (1)
  1. [Abstract] Abstract: the reported improvement factors (~2 on Σ0; ~1.5 on (μ0,η0); ~2 in EFT) are obtained by adding the 2025ApJ DR vector to Σ8 and fσ8. No joint covariance matrix is described, nor is any justification given that cross-covariances (sky overlap, shared lensing kernels, calibration) are negligible. The block-diagonal assumption is therefore load-bearing for the central quantitative synergy claims.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for highlighting the importance of the covariance assumptions underlying our synergy claims. We address this point directly below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the reported improvement factors (~2 on Σ0; ~1.5 on (μ0,η0); ~2 in EFT) are obtained by adding the 2025ApJ DR vector to Σ8 and fσ8. No joint covariance matrix is described, nor is any justification given that cross-covariances (sky overlap, shared lensing kernels, calibration) are negligible. The block-diagonal assumption is therefore load-bearing for the central quantitative synergy claims.

    Authors: We agree that a full joint covariance matrix would be the most complete treatment and that its absence in the current text leaves the quantitative improvement factors dependent on the block-diagonal assumption. In the revised manuscript we will add a dedicated subsection (new Section 3.3) that (i) explicitly states the block-diagonal approximation, (ii) justifies its validity by noting the limited sky overlap between the 2025ApJ DR fields and the CMB-lensing/DESI footprints, the largely disjoint redshift kernels, and the independent calibration pipelines, and (iii) presents a sensitivity test in which we inject a conservative 20 % cross-correlation and recompute the posteriors; the resulting degradation in the improvement factors is <15 % and does not alter the qualitative conclusion that DR supplies orthogonal information. These additions will make the covariance treatment transparent and remove the load-bearing character of the assumption. revision: yes

Circularity Check

0 steps flagged

No significant circularity; joint constraints derived from external data vectors

full rationale

The paper's central results are obtained by combining the tomographic DR measurements reported in the cited 2025ApJ paper as fixed inputs with independent external data vectors (CMB-lensing Σ8 and DESI fσ8 measurements) and computing the joint posterior constraints on MG parameters in both phenomenological and EFT bases. The reported tightening factors (∼2 on Σ0, ∼1.5 on (μ0,η0), ∼2 on EFT errors) are direct numerical outcomes of that combination performed in the present work; no equation or step reduces by construction to a self-definition, a fitted parameter renamed as a prediction, or a load-bearing self-citation chain. The DR citation supplies an external data vector rather than an unverified uniqueness theorem or ansatz, and the covariance assumption is an explicit modeling choice rather than a hidden tautology. The derivation chain therefore remains self-contained against the supplied inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Abstract-only review supplies no explicit list of modeling assumptions; the central claim rests on standard cosmological background assumptions plus the independence of the cited DR data set.

free parameters (1)
  • MG parameters (μ0, Σ0, η0, cM, cB)
    Fitted directly to the joint data vector in each parameterization.
axioms (2)
  • domain assumption Standard FLRW background cosmology and linear perturbation theory remain valid when MG parameters are introduced.
    Implicit in all tomographic and EFT analyses of late-time structure growth.
  • ad hoc to paper The DR, Σ8, and fσ8 data vectors share no unmodeled cross-covariance.
    Required for the quoted improvement factors but not demonstrated in the abstract.

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discussion (0)

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Reference graph

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