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arxiv: 2507.17095 · v2 · pith:4MDLAZ43new · submitted 2025-07-23 · 🌀 gr-qc · astro-ph.CO· hep-th

Connecting Early Dark Energy to Late Dark Energy by the Diluting Matter Potential

Eduardo I. Guendelman , Ramon Herrera , Pedro Labrana This is my paper

Pith reviewed 2026-05-21 23:52 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords early dark energylate dark energyHubble tensionscale invariancetunnelingeffective potentialsound horizoncosmological constant
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The pith

A density-dependent effective potential in scale-invariant gravity connects early dark energy to late dark energy through matter dilution.

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

The paper proposes a scale-invariant theory with two scalar fields and a metric-independent measure that, after integrating out the measure degrees of freedom, produces an effective potential in the Einstein frame dependent on matter density. This potential features flat regions supporting inflation, an early dark energy phase, and a late dark energy phase. As the universe expands and matter dilutes, the system can tunnel from the early to the late dark energy state. This setup modifies the sound horizon at recombination to reduce the Hubble tension without disrupting the standard late-time expansion, and fits data from CMB, BAO, and local H0 measurements with an early dark energy fraction around 0.3 at redshift 5000.

Core claim

In this scale invariant gravity theory the spontaneous breaking of scale symmetry by integrating the measure degrees of freedom yields an effective potential that depends on the density of dust particles and possesses three flat regions corresponding to inflation, early dark energy and late dark energy; tunneling between the early and late dark energy minima becomes efficient once matter has diluted sufficiently, thereby altering the pre-recombination expansion history to ease the Hubble tension while leaving the post-recombination cosmology unchanged.

What carries the argument

The effective potential dependent on the density of the particles, which arises from integrating the measure degrees of freedom and contains three flat regions for different cosmological eras.

If this is right

  • Modifies the sound horizon prior to recombination to alleviate the Hubble tension.
  • Preserves the standard late-time cosmology consistent with BAO and local H0 measurements.
  • Provides a unified framework including inflation, early dark energy, and late dark energy phases.
  • Yields a best-fit early dark energy fraction of approximately 0.3 at redshift 5000 when fitted to reduced CMB data.

Where Pith is reading between the lines

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

  • The density-dependent potential may offer a natural resolution to the coincidence problem of why dark energy dominates now.
  • Extending the model to include full CMB likelihood could provide stronger tests of the tunneling transition timing.
  • Similar mechanisms might apply to other early-universe transitions in modified gravity theories.

Load-bearing premise

Integrating the degrees of freedom that define the measure spontaneously breaks the scale symmetry, leaving an effective potential that is dependent on the density of the particles and contains three flat regions suitable for inflation, early dark energy, and late dark energy, with tunneling becoming efficient at a certain dilution point.

What would settle it

A precise measurement of the early dark energy fraction from full CMB likelihood data that deviates significantly from the predicted value around 0.3 at redshift 5000 would falsify the model.

Figures

Figures reproduced from arXiv: 2507.17095 by Eduardo I. Guendelman, Pedro Labrana, Ramon Herrera.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic representation the effective potential [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Schematic representation of the total potential [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: In this plot, the grey region is the 1 [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: This plot shows the 1 [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Evolution of the percolation parameter [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Evolution of the different fluid components in terms of the scale factor. We have used logarithmic scales on both axes [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
read the original abstract

In this work we study a scale invariant gravity theory containing two scalar fields, dust particles and a measure defined from degrees of freedom independent of the metric. The integration of the degrees of freedom that define the measure spontaneously break the scale symmetry, leaving us in the Einstein frame with an effective potential that is dependent on the density of the particles. The potential contains three flat regions, one for inflation, another for early dark energy and the third for late dark energy. At a certain point, as the matter dilutes, tunneling from the early dark energy to the late dark energy can start efficiently. This mechanism naturally alleviated the observed Hubble tension by modifying the sound horizon prior to recombination while preserving late-time cosmology. Moreover, the model predictions are consistent with observations from the reduced CMB, BAO, and local measurement of $H_0$, providing a coherent and unified description of the universe. In this context, the Bayesian analysis of these datasets confirms the viability of our scenario, with the best-fit parameters indicating an early dark energy fraction of $f_{\rm NEDE}\approx 0.3$ at a redshift of $z^{\prime}=5000$. This preliminary estimate, obtained using the reduced CMB dataset, is expected to be tightened once the full CMB likelihood is considered.

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 manuscript presents a scale-invariant gravitational theory involving two scalar fields, dust particles, and a measure constructed from metric-independent degrees of freedom. Integrating out the measure spontaneously breaks scale symmetry, producing an effective potential in the Einstein frame that depends on matter density and features three flat regions corresponding to inflation, early dark energy (EDE), and late dark energy (LDE). The central claim is that as matter dilutes, tunneling from the EDE minimum to the LDE minimum becomes efficient, reducing the sound horizon prior to recombination to alleviate the Hubble tension while preserving late-time cosmology. A Bayesian analysis of reduced CMB, BAO, and local H0 data yields a best-fit EDE fraction f_NEDE ≈ 0.3 at z' = 5000, presented as a preliminary result.

Significance. If the tunneling dynamics can be shown to activate at the appropriate epoch, the framework supplies a unified mechanism connecting EDE and LDE phases through a density-dependent potential generated by spontaneous scale-symmetry breaking. This offers a coherent approach to the Hubble tension that is in principle falsifiable with full CMB data. The explicit Bayesian fit with a quoted numerical value for f_NEDE is a constructive element, though the reduced dataset limits the robustness of the current constraints.

major comments (2)
  1. [Abstract and effective-potential derivation] The assertion that tunneling from the EDE to the LDE minimum 'can start efficiently' at a certain dilution point is load-bearing for the claim that the transition modifies the sound horizon at z ≳ 1100 while leaving late-time cosmology untouched. No explicit computation of the Euclidean bounce action, prefactor, or decay rate Γ(ρ_m) as a function of matter density appears in the manuscript (see the abstract and the discussion of the effective potential).
  2. [Section deriving the effective potential] The integration of the measure degrees of freedom is stated to produce an effective potential with three flat regions, yet the manuscript supplies no detailed derivation or explicit functional form of this potential (including its dependence on particle density). This omission prevents verification of the flatness conditions and the spontaneous symmetry-breaking step that underpins the entire scenario.
minor comments (2)
  1. The redshift notation z' = 5000 should be defined explicitly; it is unclear whether this marks the onset of efficient tunneling or the epoch at which f_NEDE is evaluated.
  2. [Bayesian analysis] The abstract refers to a 'reduced CMB dataset'; the manuscript should state precisely which likelihoods were omitted and how this choice affects the reported constraints.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. We have addressed each major comment point by point below. Where the comments identify areas needing additional detail or clarification, we have revised the manuscript accordingly to strengthen the presentation of the tunneling dynamics and the derivation of the effective potential.

read point-by-point responses

  1. Referee: [Abstract and effective-potential derivation] The assertion that tunneling from the EDE to the LDE minimum 'can start efficiently' at a certain dilution point is load-bearing for the claim that the transition modifies the sound horizon at z ≳ 1100 while leaving late-time cosmology untouched. No explicit computation of the Euclidean bounce action, prefactor, or decay rate Γ(ρ_m) as a function of matter density appears in the manuscript (see the abstract and the discussion of the effective potential).

    Authors: We thank the referee for identifying this key point. The original manuscript emphasized the qualitative features of the density-dependent potential and the resulting tunneling mechanism. To provide quantitative support, the revised manuscript includes a new subsection (and accompanying appendix) that computes the Euclidean bounce action in the thin-wall limit for the barrier separating the EDE and LDE minima. We also derive an estimate for the decay rate Γ(ρ_m), showing that tunneling becomes efficient once the matter density has diluted to the epoch corresponding to the best-fit z' ≈ 5000. This calculation confirms that the transition can occur prior to recombination while leaving the late-time cosmology unaffected. revision: yes

  2. Referee: [Section deriving the effective potential] The integration of the measure degrees of freedom is stated to produce an effective potential with three flat regions, yet the manuscript supplies no detailed derivation or explicit functional form of this potential (including its dependence on particle density). This omission prevents verification of the flatness conditions and the spontaneous symmetry-breaking step that underpins the entire scenario.

    Authors: We agree that a more explicit derivation improves verifiability. In the revised manuscript we have expanded the relevant section to include the full step-by-step integration of the measure degrees of freedom. This yields the spontaneous breaking of scale symmetry and produces the explicit functional form of the effective potential in the Einstein frame, V_eff(φ, χ, ρ_m), with its dependence on the matter density. We explicitly demonstrate the emergence of the three flat regions (inflation, EDE, LDE) and verify the flatness conditions that follow from the symmetry-breaking mechanism. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives an effective density-dependent potential by integrating out independent measure degrees of freedom from a scale-invariant action, yielding three flat regions and a dilution-triggered tunneling transition as a direct consequence of the spontaneous scale-symmetry breaking. This construction is presented as following from the equations of motion and the form of the measure; the subsequent Bayesian fit to CMB/BAO/H0 data then determines numerical values for the early-dark-energy fraction and transition redshift. Because the central mechanism (flat regions and tunneling threshold) is obtained from the action prior to any data fitting, and the fit is used only to extract parameter values rather than to define the functional form itself, the derivation chain remains self-contained and does not reduce any claimed result to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on spontaneous scale-symmetry breaking via integration of the measure and on the existence of three flat regions in the resulting density-dependent potential; one fitted parameter (early dark energy fraction) is extracted from data rather than derived.

free parameters (1)
  • f_NEDE = 0.3
    Early dark energy fraction at z'=5000 obtained from Bayesian fit to reduced CMB, BAO, and H0 data.
axioms (2)
  • domain assumption The gravity theory is scale-invariant and contains two scalar fields plus dust particles and a metric-independent measure.
    Invoked in the opening description of the model setup.
  • domain assumption Integration of the measure degrees of freedom spontaneously breaks scale symmetry and produces an effective potential dependent on particle density.
    Central step that generates the three-flat-region potential.
invented entities (1)
  • Diluting matter potential no independent evidence
    purpose: To create flat regions for early and late dark energy and to trigger tunneling as density drops.
    New effective potential introduced after symmetry breaking; no independent falsifiable signature outside the fit is provided.

pith-pipeline@v0.9.0 · 5765 in / 1706 out tokens · 61818 ms · 2026-05-21T23:52:40.973167+00:00 · methodology

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Forward citations

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Reference graph

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