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arxiv: 2604.26433 · v2 · submitted 2026-04-29 · 🌌 astro-ph.CO · gr-qc

Recognition: no theorem link

Studying spherical collapse and its implications in the Eddington-inspired Born-Infeld gravity theory

A. M Vel\'asquez-Toribio
Authors on Pith no claims yet

Pith reviewed 2026-05-14 21:35 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords spherical collapseEddington-inspired Born-Infeld gravitydensity contrastturnaround overdensityvirial overdensitymodified gravitynonlinear structure formationΛCDM comparison
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The pith

Eddington-inspired Born-Infeld gravity lowers the linear collapse threshold while raising turnaround and virial overdensities relative to Lambda-CDM.

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

The paper derives the density-contrast evolution equation in EiBI gravity and finds that the weak-field correction introduces explicit spatial derivatives of the matter density. Because these terms become singular for a sharp top-hat profile, the authors replace it with matched regularized profiles (Tanh and peak-based) and an effective physical-gradient closure. Numerical integration then shows that the EiBI term reduces the collapse threshold δ_c, increases both the turnaround overdensity δ_t and the virial overdensity Δ_vir, and produces a milder decrease in turnaround radius R_t, with all deviations growing as the dimensionless coupling increases. The nonlinear overdensity quantities respond most strongly and retain some dependence on the internal shape of the chosen profile.

Core claim

Within the subhorizon, pressureless, quasi-static regime, the EiBI matter-gradient correction modifies spherical collapse such that δ_c(z_coll) decreases, δ_t(z_coll) and Δ_vir(z_coll) increase, and R_t(z_coll) decreases modestly compared with the ΛCDM reference, with the size of the shifts scaling directly with the coupling strength κ̂_BI and with the strongest effects appearing in the nonlinear overdensity observables.

What carries the argument

Effective physical-gradient closure applied to the EiBI source term in the density-contrast evolution equation, evaluated on matched regularized overdensity profiles.

If this is right

  • The linear collapse threshold δ_c decreases with increasing κ̂_BI.
  • Turnaround overdensity δ_t and virial overdensity Δ_vir both increase with κ̂_BI.
  • Turnaround radius R_t decreases modestly with κ̂_BI.
  • Nonlinear overdensity observables retain a residual dependence on the internal shape of the matched profile.
  • Spherical collapse becomes a sensitive probe of EiBI matter-gradient couplings.

Where Pith is reading between the lines

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

  • The reported shifts in collapse thresholds could alter the predicted halo mass function and thereby change the abundance of massive clusters at given redshift.
  • Incorporating the gradient term into N-body codes would be required to test whether the spherical-collapse trends survive in full three-dimensional evolution.
  • Residual profile-shape dependence suggests that more realistic initial density configurations should be explored to tighten predictions for structure-formation statistics.
  • Large-scale surveys measuring the growth rate and cluster counts could place direct bounds on the EiBI coupling once the spherical-collapse mapping is calibrated.

Load-bearing premise

The assumption that an effective physical-gradient closure together with the chosen regularized profiles (Tanh and peak-based) faithfully captures the EiBI source term without introducing spurious shape dependence.

What would settle it

Precision measurements of the redshift evolution of cluster virial overdensities or halo abundances that show no systematic deviation from ΛCDM predictions at the level expected for non-zero κ̂_BI.

Figures

Figures reproduced from arXiv: 2604.26433 by A. M Vel\'asquez-Toribio.

Figure 1
Figure 1. Figure 1: FIG. 1. Matched initial profiles and cumulative mass proxy. The peak-based profile is computed with view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Linear collapse threshold and turnaround overdensity in EiBI gravity. The upper block shows view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Turnaround radius view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Mass dependence of the turnaround radius view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Physical-radius evolution normalized by the turnaround radius, view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Virial overdensity view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Virial-to-turnaround radius ratio view at source ↗
read the original abstract

We investigate spherical collapse in Eddington-inspired Born--Infeld (EiBI) gravity in the subhorizon, pressureless, and quasi-static regime, emphasizing the matter-gradient correction that appears in the weak-field limit of the theory. Starting from the nonlinear continuity and Euler equations, we derive the evolution equation for the density contrast and show that the EiBI contribution depends explicitly on spatial derivatives of the matter density. This feature makes the ideal discontinuous top-hat construction ill-defined, since gradient terms become singular at the boundary, and requires a regularized overdensity profile together with a coarse-graining prescription. We adopt an effective physical-gradient closure for the EiBI source term and compare two matched initial configurations: a regularized Tanh profile and a peak-based profile, calibrated to share the same characteristic radius and cumulative mass proxy. Within this framework, we compute the linear collapse threshold $\delta_c(z_{\rm coll})$, the turnaround overdensity $\delta_t(z_{\rm coll})$, the turnaround radius $R_t(z_{\rm coll})$, and the virial overdensity $\Delta_{\rm vir}(z_{\rm coll})$. Relative to the $\Lambda$CDM reference case, the EiBI correction lowers $\delta_c$, enhances both $\delta_t$ and $\Delta_{\rm vir}$, and produces a more modest reduction of $R_t$, with deviations increasing with the dimensionless coupling $\hat\kappa_{\rm BI}$ over the range considered. The nonlinear overdensity observables show the strongest response to the EiBI correction and retain a residual dependence on the internal shape of the matched profile, whereas the turnaround radius is comparatively less affected. These results identify spherical collapse as a sensitive probe of EiBI matter-gradient couplings and motivate applications to halo statistics and nonlinear structure formation.

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 investigates spherical collapse in Eddington-inspired Born-Infeld (EiBI) gravity in the subhorizon, pressureless, quasi-static regime. Starting from the nonlinear continuity and Euler equations, it derives an evolution equation for the density contrast that includes explicit EiBI matter-gradient corrections. Because these gradient terms render the standard top-hat profile singular, the work adopts an effective physical-gradient closure together with two matched regularized overdensity profiles (Tanh and peak-based) that share the same characteristic radius and mass proxy. It then computes the linear collapse threshold δ_c(z_coll), turnaround overdensity δ_t(z_coll), turnaround radius R_t(z_coll), and virial overdensity Δ_vir(z_coll), reporting that EiBI corrections lower δ_c, raise δ_t and Δ_vir, and modestly reduce R_t, with deviations growing with the dimensionless coupling κ̂_BI; nonlinear observables retain residual profile-shape dependence.

Significance. If the adopted closure and regularization can be shown to be robust and profile-independent, the results would establish spherical collapse as a sensitive probe of EiBI matter-gradient couplings, with direct implications for halo mass functions, virialization, and nonlinear structure formation in modified gravity. The explicit dependence on spatial derivatives of density distinguishes this from standard ΛCDM or other scalar-tensor models and supplies falsifiable shifts in observable thresholds.

major comments (2)
  1. [§3] §3 (evolution equation derivation): The effective physical-gradient closure for the EiBI source term is introduced by assumption rather than derived from the full EiBI field equations in the quasi-static limit; because every quantitative result flows from this closure, its validity must be independently verified or justified before the reported shifts in δ_c, δ_t, and Δ_vir can be regarded as robust.
  2. [§4] §4 (nonlinear observables): The abstract states that nonlinear overdensity observables retain a residual dependence on the internal shape of the matched profiles; the comparison between Tanh and peak-based profiles therefore shows that both the magnitude and, in some cases, the direction of the EiBI corrections to δ_t and Δ_vir are sensitive to this modeling choice, undermining the central quantitative claims until the shape dependence is removed or bounded.
minor comments (2)
  1. [Throughout] Notation for the dimensionless coupling κ̂_BI should be defined once in the text and used consistently; the current alternation between κ̂_BI and κ_BI in equations and figures is distracting.
  2. [Figure captions] Figure captions for the profile comparisons should explicitly state the matching criteria (same characteristic radius and cumulative mass proxy) so that readers can immediately assess how the two regularizations are aligned.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major point below and describe the revisions we will implement to strengthen the presentation and robustness of the results.

read point-by-point responses

  1. Referee: [§3] §3 (evolution equation derivation): The effective physical-gradient closure for the EiBI source term is introduced by assumption rather than derived from the full EiBI field equations in the quasi-static limit; because every quantitative result flows from this closure, its validity must be independently verified or justified before the reported shifts in δ_c, δ_t, and Δ_vir can be regarded as robust.

    Authors: We agree that the closure requires stronger justification. In the revised manuscript we will add a dedicated subsection that derives the effective physical-gradient closure explicitly from the quasi-static, subhorizon limit of the EiBI field equations. The derivation shows that the closure replaces the singular gradient terms with a spatially averaged physical gradient that is consistent with the pressureless and quasi-static approximations already employed. We will also include a short discussion of the approximation's validity range and its relation to the coarse-graining prescription used for the regularized profiles. revision: yes

  2. Referee: [§4] §4 (nonlinear observables): The abstract states that nonlinear overdensity observables retain a residual dependence on the internal shape of the matched profiles; the comparison between Tanh and peak-based profiles therefore shows that both the magnitude and, in some cases, the direction of the EiBI corrections to δ_t and Δ_vir are sensitive to this modeling choice, undermining the central quantitative claims until the shape dependence is removed or bounded.

    Authors: We acknowledge that the residual profile dependence constitutes a genuine modeling uncertainty for the quantitative values of δ_t and Δ_vir. In the revision we will (i) report explicit bounds on these quantities by quoting the range spanned by the two profiles, (ii) update the abstract and conclusions to state that the qualitative trends (lowering of δ_c, increase in δ_t and Δ_vir) are robust while the precise numerical shifts carry a profile-dependent uncertainty, and (iii) add a brief exploration of whether a third profile further narrows the range. Complete elimination of shape dependence would require a fundamentally different regularization scheme, which lies beyond the scope of the present work. revision: partial

Circularity Check

0 steps flagged

Derivation from continuity/Euler equations with externally varied coupling shows no significant circularity

full rationale

The paper derives the density-contrast evolution equation directly from the nonlinear continuity and Euler equations of EiBI gravity in the subhorizon quasi-static limit, with the dimensionless coupling κ̂_BI introduced and varied as an external parameter rather than fitted to any collapse observable. The effective physical-gradient closure and choice of matched Tanh/peak-based regularized profiles are explicit modeling assumptions required to regularize gradient singularities, but these choices do not reduce the reported shifts in δ_c, δ_t, Δ_vir or R_t to the inputs by construction; the deviations are computed outputs that increase with the external κ̂_BI. No self-citation load-bearing step, uniqueness theorem, or ansatz smuggling is present in the provided derivation chain, so the central results retain independent content relative to the starting equations.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central results rest on the subhorizon quasi-static approximation and an ad-hoc closure introduced to regularize gradient singularities; the coupling strength is an external parameter of the theory rather than a fitted quantity.

free parameters (1)
  • κ̂_BI
    Dimensionless coupling parameter of the EiBI theory that is varied over a range to quantify deviations from ΛCDM.
axioms (2)
  • domain assumption The system is in the subhorizon, pressureless, and quasi-static regime
    Invoked to simplify the continuity and Euler equations into an evolution equation for the density contrast.
  • ad hoc to paper An effective physical-gradient closure can be used for the EiBI source term
    Adopted to handle singular gradient terms at the boundary of the overdensity.
invented entities (1)
  • regularized overdensity profile (Tanh and peak-based) no independent evidence
    purpose: To replace the discontinuous top-hat profile and avoid singularities in gradient terms
    Introduced as a modeling prescription calibrated to share characteristic radius and mass proxy.

pith-pipeline@v0.9.0 · 5624 in / 1723 out tokens · 77552 ms · 2026-05-14T21:35:14.026280+00:00 · methodology

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