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Deep voids in modified gravity are governed by a single non-linear evolution equation whose effective coupling is always unscreened in voids, and the requirement of a real fifth force excludes most of the currently favored Galileon paramete

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2026-08-02 22:10 UTC pith:OR54LOUL

load-bearing objection A transparent MG extension of void hydrodynamics with a sharp unscreened-void hierarchy and a strong parameter-space filter; the main caveat is the unquantified QSA error in deep voids. the 2 major comments →

arxiv 2602.17644 v2 pith:OR54LOUL submitted 2026-02-19 astro-ph.CO gr-qc

Cosmic voids evolution in modified gravity via hydrodynamics

Tommaso Moretti , Noemi Frusciante , Giovanni Verza , Francesco Pace This is my paper
classification astro-ph.CO gr-qc
keywords cosmic voidsmodified gravityVainshtein screeningGalileon gravityvoid evolutionquasi-static approximationvoid size functioneffective field theory of dark energy
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 extends a spherical hydrodynamical description of cosmic voids to modified gravity by encoding gravity changes in effective couplings that enter the Euler and Poisson equations, yielding a non-linear evolution equation for the Eulerian density contrast driven by a time- and density-dependent effective gravitational strength. Applied to luminal Galileon theories with Vainshtein screening, it finds that inside voids the non-linear coupling always exceeds the linear one—voids are unscreened—whereas halos are screened. It then converts the possibility of an imaginary fifth force in deep underdensities into a viability filter: requiring 1 + f_MG δE ≥ 0 for every admissible void depth excludes most of the currently favored parameter space, leaving only about 18% viable, and gives a redshift-dependent minimum void depth. For viable models, modified gravity produces O(10%) coupling changes, percent-level shifts in void density evolution, and sub-percent changes in the Lagrangian-to-Eulerian mapping and shell-crossing thresholds.

Core claim

The central discovery is that for luminal Galileon theories described in the EFT of dark energy and modified gravity, under the quasi-static approximation, the non-linear void dynamics is controlled by the effective coupling µ_NL(a,R), and the physical branch of this coupling obeys µ_L < µ_NL ≤ 2µ_L − ω for voids, while halos obey µ_L > µ_NL. Hence voids always lie in the unscreened regime on the physical branch, amplifying modified gravity relative to halos. From the same formula, requiring the square root in µ_NL to remain real for all physically admissible void depths (δE ≥ −1) yields the void-informed bound max f_MG(z) > 1 ⇒ model excluded, equivalent to a minimum void depth δ_min(z) = m

What carries the argument

The machinery is the non-linear gravitational coupling µ_NL(a,R), derived under the quasi-static approximation from the scalar-field equations, combined with the Vainshtein scale R_V defined via the enclosed defect mass, (R_V/R)^3 = f_MG(a) δ_E. The algebraic square-root structure of µ_NL carries the screening: for halos it suppresses the non-linear force below the linear one, while for voids it enforces µ_NL > µ_L, making voids unscreened. The reality condition 1 + f_MG δE ≥ 0 converts this branch structure into the viability filter and the minimum-depth diagnostic. A second ingredient is the Lagrangian-to-Eulerian mapping and shell-crossing condition computed from the same evolution equati

Load-bearing premise

The quasi-static approximation (dropping time derivatives of scalar perturbations, introduced in §3.2) is load-bearing: it yields the µ_NL expression, the Vainshtein scale, and the branch-reality bound; the paper's own §4.2 notes that a fully dynamical treatment breaks down at the same stage where the QSA branch becomes ill defined, so the pathology is diagnosed inside the approximation whose validity in deep voids is the contested physics.

What would settle it

Compute a spherically symmetric, fully dynamical (beyond quasi-static) solution for a top-hat void in an excluded region of the Galileon parameter space and check whether the fifth force remains real when 1 + f_MG δE < 0; if it does, the exclusion boundary is an artifact of the quasi-static reduction. Alternatively, if N-body simulations with full Vainshtein dynamics show that voids deeper than the predicted δ_min(z) retain a real fifth force, the bound is too strong.

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

If this is right

  • Most of the (α_B0, m) region currently favored by shift-symmetric scalar-tensor constraints is inconsistent with a real fifth force inside deep low-redshift voids; only about 18% of the scanned 1σ region survives.
  • The void-informed viability requirement translates into a redshift-dependent minimum void depth δ_min(z) = max(−1, −1/f_MG(z)), which is most restrictive exactly where voids are deepest and most observed, around z ≲ 1.5.
  • In viable Galileon models, voids evolve slightly faster than in w0waCDM: percent-level deepening of δE, with O(10–30%) enhancement of gravitational couplings but sub-percent effects on the Lagrangian–Eulerian mapping and shell-crossing thresholds.
  • A regular hydrodynamical evolution up to shell-crossing is not sufficient for viability: a model can pass that test and still be excluded by the void-informed criterion because realistic inner regions can trigger the imaginary fifth force.
  • The sub-percent MG corrections to shell-crossing thresholds can propagate into percent-level changes in the void size function, analogous to small shifts in halo collapse thresholds affecting the halo mass function.

Where Pith is reading between the lines

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

  • If the quasi-static result extends to fully dynamical settings, the unscreened-void hierarchy could make deep voids a competitive probe of the braiding parameter α_B0, potentially tightening current constraints beyond what linear probes achieve.
  • The 18% viability fraction depends on the conservative choice to treat every δE ≥ −1 as an admissible void configuration; filtering at observationally realistic void depths (e.g., δE ≥ −0.8) would admit a larger region, so the exclusion is an upper bound on the excluded volume rather than a hard boundary.
  • The hierarchy proof uses only the algebraic form of µ_NL plus ω = 1 for the adopted parametrization, so the result that voids are unscreened on the physical branch may generalize to other Vainshtein-screened theories with the same functional form.
  • A direct observational test would compare the predicted δ_min(z) against measured void density profiles in surveys: if voids deeper than the bound are found in an excluded region, either the quasi-static approximation or the luminal-Galileon parametrization would need revision.

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 / 3 minor

Summary. The paper extends the authors' earlier hydrodynamical description of isolated spherical voids to modified gravity by encoding gravity modifications into an effective gravitational strength mu_NL in the non-linear Eulerian density-contrast equation, Eq. (2.10). For luminal Galileon/EFT models with Vainshtein screening, it derives mu_NL in the quasi-static approximation, Eq. (3.14), introduces a void-informed viability filter, Eq. (3.22), and applies it to the (alpha_B0, m) plane from [174], finding that only about 18% of the scanned 1-sigma region survives. It then proves analytically that on the physical void branch mu_L < mu_NL <= 2 mu_L - omega, Eqs. (4.1)-(4.3), so voids are unscreened, and quantifies the resulting effects on void depth evolution, the Lagrangian-to-Eulerian mapping, and shell-crossing thresholds. The paper is transparent about one key limitation: in Sec. 4.2 it notes that the fully dynamical non-QSA treatment of [140] breaks down at the same stage where the QSA branch becomes ill-defined.

Significance. If the QSA-conditioned results hold, the paper provides a compact, physically transparent tool that maps EFT functions to void observables and yields a falsifiable, redshift-dependent minimum void depth. The analytic hierarchy proof in Sec. 4.1 is a genuine strength: it is parameter-free, verifiable from the definition of g(y), and does not rely on numerical fitting. The numerical procedure is described sufficiently for reproduction, and the reported consistency with the independent shell-crossing analysis [177] is a good sanity check. The paper also gives quantitative hierarchies that are useful for forecasts: O(10-30%) modifications in the couplings, percent-level changes in delta_E, and sub-percent changes in the mapping and shell-crossing thresholds. The main new physics claim, the void-informed viability filter and its 18% survival fraction, is interesting but heavily assumption-laden, and its robustness needs to be established. I do not see a circularity problem: Eq. (3.14) is derived from the QSA equations of [171], and the subsequent hierarchy and filter are consequences rather than inputs.

major comments (2)
  1. [Sec. 3.2; Eqs. (3.4)-(3.8), (3.14), (3.20)-(3.23)] The quasi-static approximation is the load-bearing approximation of the paper. Time derivatives of the scalar perturbation are dropped in Eqs. (3.4)-(3.8), and everything downstream -- the mu_NL expression, the Vainshtein scale, the unscreened-void hierarchy, and the viability filter -- depends on that step. Deep voids are the least Vainshtein-screened environments, so this is precisely where QSA errors should be largest. The paper's own Sec. 4.2 comparison with Winther & Ferreira [140] shows that the fully dynamical treatment breaks down at the same stage where the QSA branch becomes ill-defined, but this does not quantify the QSA error on the viable branch. I request a direct estimate, e.g., by solving the dynamical scalar equation in spherical symmetry for representative trajectories or by evaluating an adiabaticity parameter along the void evolution. Without such an estimate, the qua
  2. [Sec. 3.4; Eqs. (3.22)-(3.23)] The conservative viability filter treats every delta_E in [-1,0) as an admissible field configuration at every redshift. The headline exclusion of about 82% of the scanned [174] 1-sigma region follows from requiring 1 + f_MG delta_E >= 0 at delta_E = -1. The paper defends this by arguing qualitatively that inner void regions can approach delta_E = -1, but no calculation in the hydrodynamical model connects reachable void depths to this field-space maximum. Indeed, Fig. 3 shows that in the left-panel model shell-crossing typically occurs before delta_E = -1 is reached along the trajectory. Please provide a sensitivity study to the assumed maximum depth (e.g., thresholds delta_E = -0.8, -0.9 or a depth derived from the top-hat inner region) or otherwise demonstrate that the 18% number is not dominated by the extreme delta_E = -1 endpoint.
minor comments (3)
  1. [Eq. (3.20)] In the definition of f_MG(a), the right-hand side appears to contain an extra delta_E: it reads f_MG(a) = (32 pi / 3) G beta^2 lambda^2 \bar{rho}_m delta_E, which would make Eq. (3.20) circular and the criterion in Eq. (3.22) ill-defined. The text and figures treat f_MG as a background function of z only, so this should be corrected to f_MG(a) = (32 pi / 3) G beta^2 lambda^2 \bar{rho}_m.
  2. [Secs. 4.1-4.2; Eqs. (4.1), (4.7)] The text states 'For the parametrization adopted in eq. (3.17), omega = 1' but Eq. (3.17) specifies only alpha_B(a); alpha_M was introduced in Eq. (3.1) and is not explicitly set to zero. The hierarchy inequalities mu_L < mu_NL <= 2 mu_L - omega are actually independent of the value of omega, but the regularization branch mu_NL = 2 mu_L - 1 used in Eq. (4.7) and Fig. 9 assumes omega = 1. Please state explicitly that alpha_M = 0 (or justify M = M_pl) for this parametrization, or replace 2 mu_L - 1 with 2 mu_L - omega.
  3. [Sec. 3.4 and Fig. 2] The viability criterion Eq. (3.22) is stated for 0 <= z <= z_in with z_in = 100, but Fig. 2 plots -ln(1+z) in [-8,0], which extends to z ~ 2980. The axes should be aligned with the stated redshift range, or the integration range in Eq. (3.22) should be adjusted.

Circularity Check

0 steps flagged

No significant circularity: the central μ_NL derivation, unscreened-void hierarchy, and void-informed viability filter are constructed from stated QSA equations and external pathology inputs, not from the conclusions they are used to derive.

full rationale

The paper's derivation chain is self-contained in the relevant sense. Eq. (2.10) is the Newtonian spherical void evolution equation adapted from the authors' earlier [138], but the MG content is introduced through Eq. (3.14), a parameter-free quasi-static expression for μ_NL obtained from the Vainshtein field equations of [171]; μ_NL is not fitted to the void outputs. The 'voids always lie in an unscreened regime' result is an algebraic consequence of Eq. (3.14) on the branch y∈[-1,0), presented in Eqs. (4.1)-(4.2), rather than an assumed input. The void-informed criterion (3.22) and the minimum-depth bound δ_min(z) in Eq. (3.23) are explicitly equivalent rearrangements of the reality condition 1+fMGδE≥0, which is imported from the authors' [143] but is anchored to the independently documented imaginary-branch pathology of Galileon/Vainshtein theories [139-142]. The headline 'only about 18% viable' is a numerical scan of the externally constrained (α_B0,m) region from [174], not a fit to the same observable predictions. The Lagrangian-to-Eulerian mapping and shell-crossing thresholds are obtained by solving Eqs. (2.10)-(2.11) with initial conditions fixed to a w0waCDM target; no MG parameter is tuned to produce those results. The paper's own caveat in §4.2, citing Winther & Ferreira [140] that the fully dynamical non-QSA evolution breaks down at the same stage as the QSA branch, is a legitimate validity/error concern for deep voids, but it is a limitation of the quasi-static approximation, not a circular reduction. The self-citations [138] and [143] are load-bearing in the sense that the formalism builds on them, but they are prior parameter-free derivations with stated assumptions that do not include the target results, and they are externally anchored; under the stated rules, such citations do not constitute circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 8 axioms · 0 invented entities

The framework rests on the QSA Vainshtein equations of [171] and the spherical hydrodynamics of [138]. The main free quantities are the scanned MG parameters (alpha_B0, m) taken from the [174] 1-sigma region, plus the initial void depth delta_v,in calibrated by shooting to a target delta_E(z=0) = -0.5 in the reference cosmology; the background parameters (w0 = -0.97, wa = -0.11, Omega_m,0 = 0.32) are treated as prior-fitted inputs and not counted as free. The most consequential axiom is the conservative void-informed reality filter (Eq. 3.22), whose strength sets the 82%-exclusion headline. No new entities (particles, forces, dimensions) are introduced; the 'imaginary fifth force' is a known branch pathology of the QSA Vainshtein solution, not an invented mechanism.

free parameters (4)
  • alpha_B0 (braiding amplitude) = 0.3-0.9 (scanned; best fit 0.6 per [174])
    Amplitude in alpha_B(a) = alpha_B0 (H0/H)^{4m} (Eq. 3.17); scanned over the [174] 1-sigma region and central to the viability, coupling, and density-evolution results.
  • m (braiding redshift-evolution power) = 2.0-2.8 (scanned; best fit 2.4 per [174])
    Controls the time evolution of alpha_B; scanned over the [174] 1-sigma region; the late-time amplification of mu_L and mu_NL depends on it.
  • delta_v,in (initial void depth) = negative; set by shooting so delta_E(z=0) = -0.5 in w0waCDM
    Initial condition at a_in = 10^-7 (Eq. 2.13), calibrated per model; all MG-vs-GR deviations are quoted with fixed ICs, making the comparison well defined but dependent on this normalization.
  • Target final void depth delta_E(z=0) = -0.5 = -0.5 (chosen)
    Representative of typical voids from simulations and surveys (§4.1, refs [92,102,179-181]); sets the IC calibration and therefore the absolute scale of the quoted percent-level deviations.
axioms (8)
  • domain assumption Quasi-static approximation for the scalar perturbation (time derivatives neglected)
    Section 3.2, Eqs. 3.4-3.9: the mu_NL expression and the pathological-branch criterion are derived within QSA; [140] shows full-dynamical evolution can break down where QSA becomes ill-defined, so the diagnostic apparatus is QSA-conditioned.
  • domain assumption Spherical symmetry; pressureless dust matter; smooth dark-energy background
    Section 2: the fluid equations (2.4)-(2.5) and the Poisson relations (2.8)-(2.9) assume these; baryonic physics, velocity anisotropy, and DE perturbations are excluded.
  • domain assumption Inverse top-hat initial profile is preserved by the evolution
    Section 2.3: requires mu_NL to depend only on (a, delta_E), not on radius for the models considered; explicit radial dependence is declared out of scope.
  • domain assumption omega = M_pl^2/M^2 = 1 for the parametrization of Eq. 3.17
    Section 4.1: asserted, not derived in-text; needed for the void/halo hierarchy inequalities (Eqs. 4.2-4.3) and the unscreened-void claim. Presumably inherited from shift-symmetric Horndeski relations in [174] but not shown.
  • ad hoc to paper Conservative void-informed criterion: max_{0<=z<=100} f_MG(z) <= 1, treating every delta_E >= -1 as an admissible configuration
    Eq. 3.22, from the authors' [143]; the 82%-exclusion headline is directly set by this interpretive choice, which the paper itself flags as potentially overly conservative.
  • domain assumption Early-time linear ICs with decaying mode neglected
    Eq. 2.13: delta'_E(a_in) = delta_E(a_in) = delta_v,in at a_in = 10^-7; validity argued in [138].
  • standard math QSA Vainshtein/Horndeski equations of Kimura et al. 2012 [171] are correct on sub-horizon scales
    Section 3.2: the scalar-field equation (3.8), the Vainshtein scale (3.11), and the potential relations (3.4)-(3.5) are taken from [171]; this is the external anchor of the mu_NL derivation.
  • domain assumption alpha_K does not affect the observables used here
    Section 3.2: alpha_K is fixed per [168,169] on the grounds that it is unconstrained by data and does not impact constraints; used to justify not scanning it.

pith-pipeline@v1.3.0-alltime-deepseek · 34712 in / 25879 out tokens · 231579 ms · 2026-08-02T22:10:47.067104+00:00 · methodology

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read the original abstract

We present a hydrodynamical description of isolated spherical voids in modified gravity (MG), extending the standard General Relativity (GR) and dynamical dark energy treatment by encoding gravity modifications into effective couplings that enter the Euler and Poisson equations. This yields a compact non-linear evolution equation for the Eulerian density contrast, controlled by a time- and density-dependent effective gravitational strength, and provides a direct map between model functions and void observables. We apply the framework to the luminal Galileon class of models, where derivative self-interactions generate Vainshtein screening and might lead to a breakdown of the physical branch in sufficiently underdense regions. Exploiting this feature, we apply the void-informed viability requirement that translates into bounds on the theory parameter space and, equivalently, on the minimum attainable void depth as a function of redshift. For viable parameters of a concrete model, we quantify the impact of MG on isolated void evolution, the Lagrangian to Eulerian mapping, and the shell-crossing threshold. Relative to GR, we find a clear hierarchy of MG effects, with ${\cal O}(10\%)$ modifications in the gravitational couplings, percent-level shifts in the void density evolution, and sub-percent deviations in both the mapping and the shell-crossing thresholds. Moreover, within the adopted parametrization, we show analytically that voids always lie in an unscreened regime on the physical branch. Overall, the formalism provides a self-consistent route to predict void dynamics and consistency constraints in a broad class of MG models.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Rolling Galileons: Evolving Braiding Strength for Viable Dark Energy

    astro-ph.CO 2026-07 conditional novelty 7.0

    Rolling Galileon gravity, with field-dependent coupling coefficients, can produce a viable phantom-crossing dark energy with healthy void screening and an acceptable fit to expansion data.

  2. Can cosmic voids ease the Hubble tension? Local expansion in $w_0w_a$CDM

    astro-ph.CO 2026-07 conditional novelty 5.0

    A KBC-like local void lowers the SH0ES–Planck Hubble tension to about 2σ but cannot fully resolve it, and evolving dark energy shifts the required void depth by only ~1%.

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