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arxiv: 2606.00411 · v1 · pith:P75IP57Snew · submitted 2026-05-29 · 🌌 astro-ph.CO

The sound of dynamical dark energy and modified gravity

Jo\~ao Rebou\c{c}as , Guilherme Brando , Felipe T. Falciano , Vivian Miranda This is my paper

Pith reviewed 2026-06-28 20:45 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords dynamical dark energymodified gravitysound speedcosmic microwave backgroundbaryon acoustic oscillationscosmic sheargeneral relativity
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The pith

In modified gravity models the preference for dynamical dark energy correlates with deviations from general relativity at redshifts below 2.

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

The paper examines whether modified gravity scenarios can account for the dynamical dark energy signal preferred by recent distance measurements by treating the dark energy sound speed as a control parameter for perturbations. It shows that in these models the preference for evolving dark energy remains linked to departures from general relativity at z less than 2 at over 95 percent . This link persists when the sound speed is allowed to vary or become superluminal, yet disappears if a cosmological constant is assumed. Adding cosmic shear and CMB lensing measurements shifts the constraints back toward general relativity. The framework therefore uses the sound speed as a physically interpretable parameter to test modified gravity.

Core claim

In modified gravity scenarios in which the dark energy equation of state and sound speed determine modifications to matter clustering, the preference for dynamical dark energy is correlated with deviations from GR over redshifts z less than 2 at over 95 percent . The significance of these deviations is not degraded when a dynamical or superluminal sound speed is considered, but vanishes if a cosmological constant is assumed. Inclusion of cosmic shear and CMB lensing data shifts the constraints toward GR.

What carries the argument

The effective dark energy sound speed c_s^2(k,a) that controls perturbative behavior in the tested modified gravity models.

If this is right

  • The correlation between dynamical dark energy and modified gravity deviations holds for both constant and varying sound speeds.
  • Assuming a cosmological constant removes any indication of modified gravity deviations in the data.
  • Cosmic shear and CMB lensing measurements favor general relativity over the modified gravity scenarios.
  • The sound speed can be used as a free parameter to explore perturbative signatures in modified gravity without degrading the dynamical dark energy signal.

Where Pith is reading between the lines

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

  • Structure growth data appear necessary to break the degeneracy between dynamical dark energy and modified gravity effects that distance measurements alone cannot resolve.
  • Future surveys sensitive to both expansion history and perturbation growth could test whether the sound speed remains a useful discriminator between models.
  • If the correlation persists, distance-only analyses may systematically favor modified gravity when dynamical dark energy is allowed.

Load-bearing premise

The dark energy equation of state and sound speed directly determine the modifications to matter clustering in the modified gravity scenarios that are tested.

What would settle it

A data combination in which the preference for dynamical dark energy shows no correlation with modified gravity deviations when the sound speed is varied, or in which constraints remain away from general relativity even after assuming a cosmological constant.

Figures

Figures reproduced from arXiv: 2606.00411 by Felipe T. Falciano, Guilherme Brando, Jo\~ao Rebou\c{c}as, Vivian Miranda.

Figure 1
Figure 1. Figure 1: FIG. 1. Solutions for [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Relative changes in the matter power spectrum for PPF dark energy in GR (left panels) and MG with [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Relative changes on the CMB anisotropy power spectra for PPF dark energy in GR (left panels) and and MG with [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Cosmological parameter posterior contours plots [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. 1D marginalized constraints on the perturbative pa [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Distribution of [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Same as Figure [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Same as Figure [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Same as Figure [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Same as Figure [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Cosmological parameter posterior confidence contours (68% and 95% credible regions). The left plot shows the [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
read the original abstract

Different candidate models are able to reproduce the dynamical dark energy signal preferred by combinations of recent distance measurements. These models may be distinguished by the behavior of their perturbations, which are controlled by the effective sound speed $c_s^2(k,a)$. To explore correlations between the dark energy sound speed and perturbative behavior, we test modified gravity (MG) scenarios in which the dark energy equation of state and sound speed determine modifications to the clustering of matter. We investigate the impact of varying the dark energy sound speed on several cosmological quantities in both General Relativity (GR) and MG. We constrain the dark energy and modified gravity parameters using measurements of the Cosmic Microwave Background (CMB) from Planck PR4, type Ia supernova luminosity distances (SN) from Pantheon+, Baryon Acoustic Oscillations (BAO) from DESI DR2, and cosmic shear from DES-Y3. Using the combination of CMB+BAO+SN, we find that, in the MG scenarios, the preference for dynamical dark energy is correlated with deviations from GR over redshifts $z < 2$ at over 95\% confidence level. The significance of these deviations is not degraded when considering a dynamical or superluminal sound speed, but vanishes if we assume a cosmological constant. The inclusion of cosmic shear and CMB lensing data significantly shifts the constraints towards GR. Our framework enables the exploration of modified gravity models using the dark energy sound speed as a physically meaningful free parameter.

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

2 major / 2 minor

Summary. The paper claims that in modified gravity (MG) scenarios constructed such that the dark energy equation of state w(a) and sound speed cs²(k,a) determine modifications to matter clustering, combinations of Planck PR4 CMB, Pantheon+ SN, and DESI DR2 BAO data show a preference for dynamical dark energy that correlates with deviations from GR at z<2 at >95% CL. This correlation is robust to dynamical or superluminal cs² but vanishes under a cosmological constant assumption; adding DES-Y3 cosmic shear and CMB lensing shifts constraints toward GR. The framework treats cs² as a physically meaningful free parameter for exploring MG effects.

Significance. If the central mapping from (w, cs²) to MG perturbative effects holds without additional independent degrees of freedom, the work offers a concrete parametrization for linking dark energy perturbations to modified gravity clustering, using recent public datasets. The finding that lensing data degrades the GR deviation signal is a useful consistency check. However, the significance is limited by the lack of explicit verification that the tested MG scenarios are not reducible to a special case of standard MG parametrizations.

major comments (2)
  1. [MG scenarios construction (abstract and model definition sections)] The central claim (dynamical DE preference correlates with GR deviations at >95% CL in MG scenarios, robust to cs variations) rests on the construction in which w(a) and cs²(k,a) fully determine the modifications to matter clustering. The manuscript states the scenarios explicitly in the abstract but provides no perturbation equations or explicit reduction showing how cs² serves as the sole control parameter (e.g., whether independent μ(k,a) and η(k,a) functions are eliminated by construction). Without this, the reported correlation and its robustness to superluminal cs² risk being parametrization-specific rather than general.
  2. [Results section on parameter constraints] Table or figure reporting the 95% CL constraints on MG parameters with CMB+BAO+SN (and the shift upon adding lensing): the error budgets, full analysis pipeline, and covariance treatment are not detailed enough to verify whether post-hoc model choices affect the central claim that deviations vanish for Lambda but persist for dynamical DE. This is load-bearing for the robustness statement.
minor comments (2)
  1. [Model parameters] Notation for cs²(k,a) should be clarified early: is the k-dependence functional form specified, or is it assumed scale-independent in the reported runs?
  2. [Introduction or results] The abstract mentions 'several cosmological quantities' affected by varying cs²; a brief summary table or reference to the relevant figure would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below and will revise the manuscript to improve clarity and completeness.

read point-by-point responses

  1. Referee: [MG scenarios construction (abstract and model definition sections)] The central claim (dynamical DE preference correlates with GR deviations at >95% CL in MG scenarios, robust to cs variations) rests on the construction in which w(a) and cs²(k,a) fully determine the modifications to matter clustering. The manuscript states the scenarios explicitly in the abstract but provides no perturbation equations or explicit reduction showing how cs² serves as the sole control parameter (e.g., whether independent μ(k,a) and η(k,a) functions are eliminated by construction). Without this, the reported correlation and its robustness to superluminal cs² risk being parametrization-specific rather than general.

    Authors: We agree that the explicit perturbation equations and the reduction showing how w(a) and cs²(k,a) determine the MG modifications (eliminating independent μ(k,a) and η(k,a)) are not presented in sufficient detail. In the revised manuscript we will add the relevant equations in the model definition section, making clear that the MG effects on clustering are fully specified by the DE parameters by construction. This addition will also note that the reported correlation is a feature of this specific parametrization, as intended. revision: yes

  2. Referee: [Results section on parameter constraints] Table or figure reporting the 95% CL constraints on MG parameters with CMB+BAO+SN (and the shift upon adding lensing): the error budgets, full analysis pipeline, and covariance treatment are not detailed enough to verify whether post-hoc model choices affect the central claim that deviations vanish for Lambda but persist for dynamical DE. This is load-bearing for the robustness statement.

    Authors: We acknowledge that additional detail on the analysis pipeline, error budgets, and covariance treatment would strengthen the presentation. In the revised version we will expand the relevant subsection to include these elements, ensuring the robustness of the constraints (including the vanishing of deviations under a cosmological constant) can be verified directly from the text. revision: yes

Circularity Check

0 steps flagged

No significant circularity; constraints from external datasets with independent parameters

full rationale

The paper constrains dark energy and MG parameters using external public datasets (Planck PR4, Pantheon+, DESI DR2, DES-Y3) and introduces cs^2(k,a) as an independent free parameter within explicitly defined MG scenarios. No load-bearing self-citations, self-definitional reductions, or fitted inputs renamed as predictions are present. The central correlation claim follows from fitting these independent observables rather than reducing to internal definitions by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard cosmological perturbation theory in GR and MG plus the modeling choice that sound speed controls clustering modifications; no new entities are introduced.

free parameters (1)
  • dark energy sound speed cs^2(k,a)
    Introduced and varied as the physically meaningful free parameter controlling perturbative behavior in both GR and MG scenarios.
axioms (1)
  • domain assumption Cosmological perturbation theory applies to the MG models with DE equation of state and sound speed setting matter clustering modifications
    Invoked to link sound speed to observable clustering effects.

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