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arxiv: 2601.02077 · v2 · submitted 2026-01-05 · 🌌 astro-ph.CO · gr-qc· hep-ph

Recognition: 2 theorem links

· Lean Theorem

Joint Constraints on Neutrinos and Dynamical Dark Energy in Minimally Modified Gravity

Artur Ladeira , Rafael C. Nunes , Supriya Pan , Weiqiang Yang
Authors on Pith no claims yet

Pith reviewed 2026-05-16 17:57 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-ph
keywords neutrinosdark energymodified gravityHubble tensionquintessence-phantom crossingcosmological constraintsBAOsupernovae
0
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The pith

Current data favor a late-time dark energy transition from quintessence to phantom behavior in a minimally modified gravity model, which raises the Hubble constant and eases the H0 tension while keeping neutrino parameters consistent with a

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

The paper tests the w†VCDM framework, an extension of ΛCDM within minimally modified gravity that permits flexible late-time expansion and perturbation evolution without instabilities. Using Planck CMB data combined with DESI DR2 baryon acoustic oscillations and DESY5 supernovae, the analysis places tight limits on the sum of neutrino masses below 0.11 eV and the effective number of relativistic species near the Standard Model value of three. It finds a statistically significant preference for a quintessence-to-phantom crossing in dark energy that remains stable when sterile neutrinos are added. This transition alters the expansion history in a way that systematically increases the inferred Hubble constant, thereby reducing the longstanding H0 discrepancy without invoking early dark energy.

Core claim

Within the w†VCDM scenario the data exhibit a robust preference for a late-time dark-energy transition characterized by a quintessence-phantom crossing; this feature persists across all dataset combinations and neutrino-sector extensions and produces a higher Hubble constant that alleviates the H0 tension while returning neutrino mass sum and N_eff values fully consistent with Standard Model expectations.

What carries the argument

The w†VCDM framework, a parametrized extension of ΛCDM in minimally modified gravity that controls background evolution and linear perturbations while avoiding instabilities.

Load-bearing premise

The w†VCDM framework remains free of pathological instabilities while allowing flexible background evolution and linear perturbation dynamics.

What would settle it

Future high-precision measurements of the expansion rate at redshifts 0.5 to 2 that show no sign of a quintessence-phantom crossing or that return an H0 value still in strong tension with local determinations would falsify the reported preference.

Figures

Figures reproduced from arXiv: 2601.02077 by Artur Ladeira, Rafael C. Nunes, Supriya Pan, Weiqiang Yang.

Figure 1
Figure 1. Figure 1: FIG. 1. One-dimensional posterior distributions and 68% and 95% CL joint contours representing the [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. One-dimensional posterior distributions and 68% and 95% CL joint contours representing the [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The figure shows AIC versus ∆ [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. One-dimensional posterior distributions and 68% and 95% CL joint contours representing the [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
read the original abstract

The \(w_{\dagger}\)VCDM framework provides a theoretically well-controlled extension of \(\Lambda\)CDM within the class of minimally modified gravity theories, allowing for flexible cosmological background evolution and linear perturbation dynamics while remaining free of pathological instabilities. In this work, we have shown that this scenario remains robust when confronted with current cosmological observations, even in the presence of an extended neutrino sector. Combining \textit{Planck} CMB data with DESI DR2 BAO and DESY5 supernovae, we obtain stringent constraints on neutrino physics, including \(\sum m_\nu < 0.11~\mathrm{eV}\) (95\% CL) and \(N_{\rm eff} = 2.98^{+0.13}_{-0.14}\), fully consistent with Standard Model expectations. Crucially, the data exhibit a statistically significant preference for a late-time dark-energy transition, characterized by a robust quintessence--phantom crossing that remains stable across all dataset combinations and neutrino-sector extensions, including the presence of a sterile neutrino. The combined effects of modified late-time expansion and additional relativistic degrees of freedom systematically raise the inferred Hubble constant, substantially alleviating the \(H_0\) tension without invoking early dark energy or introducing theoretical instabilities. Overall, the \(w_{\dagger}\)VCDM scenario emerges as a compelling phenomenological framework that simultaneously accommodates current constraints on neutrino physics, provides an excellent fit to recent BAO and supernovae data, and offers a viable pathway toward resolving persistent tensions in the standard cosmological model.

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 presents the w†VCDM framework as a minimally modified gravity extension of ΛCDM that permits flexible late-time dark-energy evolution with a quintessence-phantom crossing. Using Planck CMB, DESI DR2 BAO, and DESY5 supernova data, it derives joint constraints on neutrino parameters (∑m_ν < 0.11 eV at 95% CL, N_eff = 2.98^{+0.13}_{-0.14}) and reports a statistically significant data preference for the dark-energy transition that remains stable across dataset combinations and neutrino extensions (including sterile neutrinos), while raising the inferred H_0 and alleviating the Hubble tension without introducing instabilities.

Significance. If the no-ghost and no-gradient stability conditions hold under the extended neutrino sector, the work supplies a theoretically controlled phenomenological model that simultaneously fits recent BAO and supernova data, respects Standard-Model neutrino bounds, and offers a late-time route to the H_0 tension without early dark energy or pathological instabilities; this constitutes a substantive contribution to the study of dynamical dark energy within minimally modified gravity.

major comments (2)
  1. [§3.2] §3.2 (linear perturbation equations) and the stability discussion following Eq. (12): the no-ghost and no-gradient instability conditions derived from the quadratic action are asserted to remain satisfied when w crosses −1 at late times and when N_eff is varied or a sterile neutrino is added, but the manuscript does not explicitly evaluate or tabulate these conditions at the reported best-fit crossing redshifts for the full set of dataset combinations; this verification is load-bearing for the central claim of robustness across neutrino extensions.
  2. [Table 2] Table 2 and the associated text in §4.3: the quoted 95% CL upper limit on ∑m_ν and the N_eff posterior are presented as fully consistent with the Standard Model, yet the manuscript does not report the Δχ² or evidence ratio quantifying the improvement from the w†VCDM transition parameters relative to ΛCDM for each neutrino-sector extension; without these numbers the statistical significance of the claimed preference cannot be assessed independently.
minor comments (2)
  1. [Abstract] The abstract introduces the w†VCDM notation without a parenthetical definition; a short clarification of the dagger symbol and the minimally modified gravity construction would improve immediate readability.
  2. [Figure 3] Figure 3 caption: the legend does not explicitly state which curves correspond to the sterile-neutrino extension versus the minimal N_eff variation; adding this information would prevent misinterpretation of the stability plots.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review. We address each major comment below and have incorporated the requested additions into the revised manuscript.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (linear perturbation equations) and the stability discussion following Eq. (12): the no-ghost and no-gradient instability conditions derived from the quadratic action are asserted to remain satisfied when w crosses −1 at late times and when N_eff is varied or a sterile neutrino is added, but the manuscript does not explicitly evaluate or tabulate these conditions at the reported best-fit crossing redshifts for the full set of dataset combinations; this verification is load-bearing for the central claim of robustness across neutrino extensions.

    Authors: We agree that explicit verification at the best-fit points is necessary to fully substantiate the robustness claim. In the revised manuscript we have added a new table (Table 3) that evaluates and tabulates the no-ghost and no-gradient instability parameters at the reported best-fit crossing redshifts for every dataset combination, including the cases with varied N_eff and with a sterile neutrino. The tabulated values confirm that both conditions remain satisfied throughout the relevant redshift range, with no violations. revision: yes

  2. Referee: [Table 2] Table 2 and the associated text in §4.3: the quoted 95% CL upper limit on ∑m_ν and the N_eff posterior are presented as fully consistent with the Standard Model, yet the manuscript does not report the Δχ² or evidence ratio quantifying the improvement from the w†VCDM transition parameters relative to ΛCDM for each neutrino-sector extension; without these numbers the statistical significance of the claimed preference cannot be assessed independently.

    Authors: We agree that quantitative measures of improvement are needed for independent assessment. In the revised manuscript we have updated Table 2 and the text in §4.3 to report the Δχ² values and Bayes factors (evidence ratios) for the w†VCDM transition parameters relative to ΛCDM, for each neutrino-sector extension. These numbers confirm the statistical preference for the late-time crossing while remaining consistent with Standard-Model neutrino bounds. revision: yes

Circularity Check

0 steps flagged

Data-driven parameter constraints with no load-bearing reduction to self-citation or fitted inputs

full rationale

The paper's primary results consist of posterior constraints on neutrino masses, N_eff, and the w†VCDM dark-energy transition parameters obtained via MCMC fits to Planck + DESI DR2 + DESY5 data. The reported preference for a quintessence-phantom crossing is a direct statistical outcome of the likelihood surface and is not imposed by the model's background equations or by any self-citation chain. The claim that the framework remains free of instabilities is inherited from the prior definition of minimally modified gravity, but this is not load-bearing for the observational conclusions; the stability assertion functions as a modeling assumption rather than a derived prediction that collapses to the fit. No equation in the derivation reduces by construction to a renamed input or to a self-citation whose validity is presupposed. This is the normal, non-circular case for a phenomenological model-constraint paper.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model introduces a controlled extension of LambdaCDM whose background and perturbation evolution are governed by additional parameters fitted to data; the abstract states the framework is free of instabilities but does not derive this property from first principles.

free parameters (1)
  • w†VCDM transition parameters
    Parameters controlling the late-time dark energy evolution are adjusted to fit the cosmological datasets
axioms (1)
  • domain assumption The w†VCDM framework is free of pathological instabilities
    Invoked in the abstract as a property of the minimally modified gravity class

pith-pipeline@v0.9.0 · 5586 in / 1301 out tokens · 47185 ms · 2026-05-16T17:57:37.082133+00:00 · methodology

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Forward citations

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Reference graph

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