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arxiv: 2509.13302 · v2 · submitted 2025-09-16 · 🌌 astro-ph.CO · gr-qc· hep-ph· hep-th

Comparing Minimal and Non-Minimal Quintessence Models to 2025 DESI Data

Husam Adam , Mark P. Hertzberg , Daniel Jim\'enez-Aguilar , Iman Khan This is my paper

Pith reviewed 2026-05-18 15:42 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-phhep-th
keywords quintessencenon-minimal couplingdark energyDESIequation of statefifth forcecosmological constraints
0
0 comments X

The pith

Non-minimal quintessence can match DESI's evolving dark energy only for specially chosen narrow couplings.

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

This paper tests whether quintessence models can explain the 2025 DESI data hinting that dark energy's equation of state is increasing over time. Minimal models with various potentials like quadratic or hilltop shapes offer only modest improvements over a simple cosmological constant. Non-minimally coupled scalar fields can produce a temporary phase where the equation of state dips below -1 before relaxing, which helps fit the data. However, the lightness of the scalar introduces fifth forces and changes in gravitational strength that are strongly limited by experiments, and only a very narrow band of coupling strengths avoids these limits.

Core claim

Various quintessence potentials provide modest fits to the DESI data, but non-minimally coupled scalars achieve better agreement by allowing an effective equation of state that temporarily obeys w < -1 and then relaxes to w > -1; since the scalar is very light, this induces a fifth force and time evolution in the effective gravitational strength, which are tightly constrained, and only a very narrow range of carefully selected non-minimal couplings evades these bounds.

What carries the argument

Non-minimal coupling between the quintessence scalar field and gravity, which alters the effective dark energy equation of state while introducing fifth-force interactions and time-dependent gravitational constant.

If this is right

  • Some quintessence potentials improve the fit to DESI data modestly compared to a cosmological constant.
  • Non-minimal coupling enables a transient phantom equation of state w < -1 that better matches the observed evolution.
  • Light scalars in these models produce fifth forces and varying effective G that must satisfy existing gravity tests.
  • Generic non-minimal couplings violate gravity constraints, while only narrow specially chosen values remain viable.

Where Pith is reading between the lines

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

  • Future precision measurements of gravitational strength over cosmic time could directly test the allowed narrow coupling window.
  • Such tuning might point to underlying symmetries or selection mechanisms in fundamental theory that pick out these specific values.
  • Similar non-minimal effects could be explored in other dynamical dark energy scenarios beyond quintessence.

Load-bearing premise

The non-minimal coupling strength can be restricted to a very narrow, specially chosen range that simultaneously fits the DESI data and satisfies all existing fifth-force and time-varying-G constraints without introducing other unobserved effects.

What would settle it

Detection of a fifth force or variation in G at a level that rules out the narrow window of couplings needed to fit the DESI data while satisfying current bounds.

Figures

Figures reproduced from arXiv: 2509.13302 by Daniel Jim\'enez-Aguilar, Husam Adam, Iman Khan, Mark P. Hertzberg.

Figure 1
Figure 1. Figure 1: FIG. 1. Potentials [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Top left: Value of the scalar field as a function of time. Top right: Fractional energy [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Equation of state parameters [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Equation of state parameters [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Equation of state parameters [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Top left: DESI 2 [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Top left: Value of the scalar field as a function of time. Top right: Fractional energy [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Solar System (left) and effective gravitational constant (right) constraints versus time. The [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Time evolution of the effective gravitational constant. The vertical dotted line corresponds [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
read the original abstract

In this work we examine the 2025 DESI analysis of dark energy, which suggests that dark energy is evolving in time with an increasing equation of state $w$. We explore a wide range of quintessence models, described by a potential function $V(\varphi)$, including: quadratic potentials, quartic hilltops, double wells, cosine functions, Gaussians, inverse powers. We find that while some provide improvement in fitting to the data, compared to a cosmological constant, the improvement is only modest. We then consider non-minimally coupled scalars which can help fit the data by providing an effective equation of state that temporarily obeys $w<-1$ and then relaxes to $w>-1$. Since the scalar is very light, this leads to a fifth force and to time evolution in the effective gravitational strength, which are both tightly constrained by tests of gravity. For a very narrow range of carefully selected non-minimal couplings we are able to evade these bounds, but not for generic values.

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 compares minimal and non-minimal quintessence models with potentials including quadratic, quartic hilltop, double-well, cosine, Gaussian, and inverse-power forms to the 2025 DESI data suggesting a time-evolving dark energy equation of state w that is increasing. Minimal models yield only modest improvements over a cosmological constant. Non-minimal couplings can produce a temporary effective w < -1 before relaxing to w > -1, but the very light scalar induces fifth forces and time-varying effective G that are tightly constrained by gravity tests; only a narrow, specially chosen range of couplings evades these bounds.

Significance. If the quantitative fit results hold, the work supplies useful constraints on quintessence parameter space in response to new DESI indications of evolving dark energy. The emphasis on the narrow viability window for non-minimal models usefully illustrates the tension between fitting w < -1 behavior and existing fifth-force/time-varying-G limits.

major comments (2)
  1. [Abstract / Results] Abstract and results section: the repeated claim of 'modest improvement' for certain minimal potentials is not accompanied by explicit quantitative fit statistics (e.g., Delta chi^2, AIC differences, or Bayesian evidence ratios relative to LambdaCDM), which are required to evaluate whether the improvement is statistically meaningful or merely marginal.
  2. [Non-minimal models] Non-minimal coupling discussion: the procedure for identifying the 'very narrow range of carefully selected non-minimal couplings' that simultaneously fit the DESI data and satisfy fifth-force and varying-G bounds is not described; the manuscript must specify the exact prior ranges, the numerical method used to isolate this window, and explicit verification that no additional unobserved effects (e.g., modified growth or screening failures) arise within it.
minor comments (2)
  1. [Methods] All potential functions V(phi) should be written explicitly with their parameter definitions and ranges in a dedicated methods subsection for reproducibility.
  2. [Figures] Figure captions and axis labels for any w(z) or likelihood plots should include the precise data points or DESI release version used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript comparing quintessence models to the 2025 DESI data. We address each of the major comments below and have made revisions to the manuscript where necessary to improve clarity and completeness.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and results section: the repeated claim of 'modest improvement' for certain minimal potentials is not accompanied by explicit quantitative fit statistics (e.g., Delta chi^2, AIC differences, or Bayesian evidence ratios relative to LambdaCDM), which are required to evaluate whether the improvement is statistically meaningful or merely marginal.

    Authors: We agree with the referee that explicit quantitative measures are important for assessing the significance of the improvements. In the revised manuscript, we will add Delta chi^2 values, AIC differences, and if feasible Bayesian evidence ratios comparing the best-fitting minimal quintessence models to LambdaCDM. This will be included in the results section and referenced in the abstract. revision: yes

  2. Referee: [Non-minimal models] Non-minimal coupling discussion: the procedure for identifying the 'very narrow range of carefully selected non-minimal couplings' that simultaneously fit the DESI data and satisfy fifth-force and varying-G bounds is not described; the manuscript must specify the exact prior ranges, the numerical method used to isolate this window, and explicit verification that no additional unobserved effects (e.g., modified growth or screening failures) arise within it.

    Authors: We acknowledge that the current manuscript does not provide a detailed description of how the narrow viable range for non-minimal couplings was determined. In the revision, we will expand the relevant section to include the exact prior ranges explored, the numerical approach (such as parameter scans or Monte Carlo methods) used to identify the window that fits the data while satisfying gravity constraints, and additional checks confirming the absence of issues like modified growth rates or failures in screening mechanisms within this parameter range. revision: yes

Circularity Check

0 steps flagged

No significant circularity in model comparisons to external data

full rationale

The paper compares a range of quintessence potentials (minimal and non-minimal) directly to 2025 DESI observations and pre-existing fifth-force/time-varying-G constraints from external tests of gravity. No central quantity such as an equation-of-state parameter, coupling strength, or fit improvement is defined in terms of itself or obtained by fitting a subset and then relabeling the same quantity as a prediction. The statement that only a narrow range of non-minimal couplings evades bounds is presented as a physical limitation drawn from independent gravity experiments, not as a result derived from the DESI fit itself. All load-bearing steps therefore remain anchored in external data and standard model-building assumptions rather than reducing to self-referential inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis rests on the standard FLRW cosmology plus scalar-field dynamics and on external experimental bounds on fifth forces and varying G; the potential parameters and coupling strengths are free parameters adjusted to the data.

free parameters (2)
  • potential parameters (mass, self-coupling, etc.)
    Parameters in quadratic, quartic, cosine, Gaussian, and inverse-power potentials are varied to improve fits to DESI data.
  • non-minimal coupling strength
    The coupling parameter is tuned within a narrow window to evade gravity constraints while attempting to match the observed w evolution.
axioms (2)
  • domain assumption The background spacetime is described by the flat FLRW metric with a homogeneous scalar field.
    Standard assumption invoked throughout quintessence cosmology.
  • domain assumption Existing solar-system and laboratory tests tightly bound fifth forces and time variation of G.
    Used to constrain the non-minimal coupling range.

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Lean theorems connected to this paper

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    Relation between the paper passage and the cited Recognition theorem.

    We explore a wide range of quintessence models, described by a potential function V(φ), including: quadratic potentials, quartic hilltops, double wells, cosine functions, Gaussians, inverse powers... non-minimally coupled scalars which can help fit the data by providing an effective equation of state that temporarily obeys w < −1

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Forward citations

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