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arxiv: 2606.28074 · v1 · pith:THM6C54Lnew · submitted 2026-06-26 · 🌌 astro-ph.CO

Dark energy perturbations and the robustness of cosmological neutrino-mass constraints

Yu-Hang Yang , Emmanuel N. Saridakis , Yi-Fu Cai , Hao-Ran Yu This is my paper

Pith reviewed 2026-06-29 03:04 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords neutrino massesdark energy perturbationscosmological constraintsdynamical dark energystructure growthredshift space distortionsneutrino mass tension
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The pith

Allowing dark energy to cluster reverses the relaxation of neutrino mass bounds seen in smooth models.

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

The paper tests whether dynamical dark energy can ease the cosmological upper limit on the sum of neutrino masses. It shows that this easing occurs only if dark energy is treated as perfectly smooth. When the clustering of dark energy is included in the calculations, the data instead favor smaller neutrino masses, sometimes even negative values. The shift comes from a trade-off in how both neutrinos and dark energy perturbations suppress the growth of cosmic structures. This makes the neutrino mass constraint depend on the details of the dark energy model used.

Core claim

Cosmological data from CMB, BAO, RSD, and supernovae indicate that including dark energy perturbations in dynamical dark energy models shifts the preferred neutrino mass sum to smaller and more negative values, in contrast to the relaxation obtained when perturbations are neglected. This occurs because neutrino free-streaming and dark energy perturbations produce similar effects on structure growth observables, allowing different combinations to fit the data equally well.

What carries the argument

The degeneracy between neutrino free-streaming and dark-energy perturbations in structure-growth observables such as redshift-space distortions.

If this is right

  • Smooth dark energy models relax the upper bounds on neutrino mass.
  • Including dark energy clustering moves the preferred neutrino mass lower.
  • Multiple pairs of neutrino mass and dark energy clustering parameters can fit the data similarly.
  • Neutrino mass constraints from cosmology are sensitive to the treatment of dark energy perturbations.
  • Consistent modeling of dark energy perturbations is required for reliable neutrino mass inference.

Where Pith is reading between the lines

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

  • Analyses of other parameters influenced by structure growth might show similar model dependencies when dark energy perturbations are added.
  • Upcoming surveys with better measurements of growth rate could help distinguish the contributions from neutrinos and dark energy.
  • The findings highlight the need to consider perturbation effects in any extension of the standard cosmological model that involves clustering components.

Load-bearing premise

The main driver of the change in neutrino mass preference is the degeneracy with dark energy perturbations rather than other modeling choices or data features.

What would settle it

If new data from redshift-space distortion surveys shows no shift in neutrino mass when dark energy perturbations are modeled, the degeneracy explanation would be falsified.

Figures

Figures reproduced from arXiv: 2606.28074 by Emmanuel N. Saridakis, Hao-Ran Yu, Yi-Fu Cai, Yu-Hang Yang.

Figure 1
Figure 1. Figure 1: A schematic illustration of the degeneracy between neutrino free-streaming and dark-energy perturbations. Different combinations of effective neutrino mass and dark-energy clustering can produce similar modifications to the growth of cosmic structures. The example shown corresponds to w = −0.85. This observation has direct implications for recent claims that dynamical dark-energy models alleviate the tensi… view at source ↗
Figure 2
Figure 2. Figure 2: Normalized one-dimensional posterior distributions of the effective neutrino mass Pmν for the ΛCDM and w0waCDM models, obtained from the combined BAO+CMB+SNe data set. The lower bounds implied by neutrino oscilla￾tion measurements are also shown for both the normal ordering (NO) and inverted ordering (IO). The left panel presents the results for smooth and clustering dark-energy models, while the right pan… view at source ↗
Figure 3
Figure 3. Figure 3: Left panel: Marginalized constraints in the (w0, wa) plane for the w0waCDM model under different perturbative descriptions. The gray line corresponds to w0 + wa = −1, while the ΛCDM point (w0 = −1, wa = 0) is located at the intersection of the axes. Right panel: Marginalized constraints in the (cB, cM) plane for the ΛCDM+EFT and w0waCDM+EFT models. The contours correspond to the 68% and 95% confidence regi… view at source ↗
Figure 4
Figure 4. Figure 4: Growth-rate measurements fσ8(z) together with the predictions of the best-fit cosmological models. Left panel: effective-fluid description. Right panel: EFT description. Despite the substantial differences in the inferred neutrino-mass constraints, the predicted growth histories remain remarkably similar, illustrating the degeneracy between neutrino free-streaming and dark-energy perturbations discussed in… view at source ↗
Figure 5
Figure 5. Figure 5: Residuals of the BAO distance measurements DM/rd (left panel) and DH/rd (right panel) relative to the Planck 2018 best-fit ΛCDM model. The curves show the predictions of the best-fit models considered in this work. Despite the different inferred neutrino-mass and dark-energy parameters, all models provide very similar BAO-distance predictions, illustrating that current observations primarily constrain dege… view at source ↗
Figure 6
Figure 6. Figure 6: Profile likelihoods for the effective neutrino mass in the ΛCDM and w0waCDM models, obtained from the combined BAO+CMB+SNe data set. The curves show parabolic fits to the profiled ∆χ 2 distributions. The shaded regions indicate the 1σ and 2σ confidence intervals, while the vertical line marks the lower bound implied by neutrino oscillation measurements for the normal ordering (NO). As shown in [PITH_FULL_… view at source ↗
Figure 7
Figure 7. Figure 7: Left panel: Normalized one-dimensional posterior distributions of the effective neutrino mass Pmν in the w0waCDM model when the dark-energy sound speed is allowed to vary freely. Results are obtained from the combined BAO+CMB+SNe data set. The lower bounds implied by neutrino oscillation measurements for the normal ordering (NO) and inverted ordering (IO) are also shown. Right panel: Normalized marginalize… view at source ↗
Figure 8
Figure 8. Figure 8: Residuals of the CMB temperature power spectrum (left panel) and the matter power spectrum at z = 0 (right panel) in the ΛCDM model for different values of the effective neutrino mass. The black solid line corresponds to the massless-neutrino case, while the blue and green curves correspond to Pmν = 0.15 eV and Pmν = −0.15 eV, respectively [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Residuals of the CMB temperature power spectrum (left panel) and the matter power spectrum at z = 0 (right panel) illustrating the impact of dark-energy perturbations. The black solid line corresponds to the ΛCDM model, while the blue and green curves correspond to the w0waCDM model with smooth (c 2 s = 1) and clustering (c 2 s = 10−5 ) dark energy, respectively. For illustration, we adopt w0 = −0.7 and wa… view at source ↗
Figure 10
Figure 10. Figure 10: Left panel: Normalized one-dimensional posterior distributions of the effective neutrino mass Pmν in the wCDM model, obtained from the combined BAO+CMB+SNe data set. The lower bounds implied by neutrino oscillation measurements for the normal ordering (NO) and inverted ordering (IO) are also shown. Right panel: Normalized marginalized posterior distribution of the equation-of-state parameter w. The prefer… view at source ↗
read the original abstract

Cosmological observations are placing increasingly stringent bounds on the sum of neutrino masses, approaching the lower limits implied by neutrino oscillation experiments. Recent studies have suggested that dynamical dark energy may alleviate this apparent tension. However, these conclusions generally rely on the assumption that dark energy remains smooth, neglecting its perturbations. In this work we investigate the robustness of cosmological neutrino-mass constraints by consistently incorporating dark-energy perturbations. Using CMB, BAO, RSD, and supernova data, we show that the commonly reported alleviation of the neutrino-mass tension in dynamical dark-energy models is not generic. While smooth dark energy substantially relaxes the neutrino-mass bounds, allowing dark energy to cluster shifts the preferred neutrino mass toward smaller, and even more negative, effective values. We demonstrate that this behavior originates from a degeneracy between neutrino free-streaming and dark-energy perturbations in structure-growth observables. Different combinations of neutrino mass and dark-energy clustering can provide similarly good fits to current data while yielding significantly different neutrino-mass constraints. Our results show that cosmological neutrino-mass measurements are inherently model dependent and that reliable neutrino-mass inference requires a consistent treatment of dark-energy perturbations.

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

1 major / 0 minor

Summary. The paper examines the robustness of cosmological upper limits on the sum of neutrino masses when dynamical dark energy is allowed to cluster. Using CMB, BAO, RSD and supernova data, it finds that the relaxation of neutrino-mass bounds previously reported for smooth dynamical dark energy disappears once dark-energy perturbations are included; instead the posterior for the neutrino mass shifts toward smaller and even negative values. The authors attribute this shift to a degeneracy between neutrino free-streaming and dark-energy clustering that is visible in the growth observables (primarily RSD).

Significance. If the central result holds, the work shows that neutrino-mass constraints from current data are sensitive to the treatment of dark-energy perturbations and are therefore more model-dependent than is commonly assumed. This has direct implications for the interpretation of the apparent tension between cosmological and oscillation bounds on the neutrino mass sum.

major comments (1)
  1. [Results / Interpretation section (exact section number not visible in abstract)] The central claim that the shift in neutrino-mass preference is driven by a degeneracy specifically in structure-growth observables (RSD and related data) is load-bearing for the interpretation. The manuscript should provide an explicit test (e.g., a run with RSD data removed) showing that the shift disappears or reverses when only CMB+BAO+SN are used, thereby isolating the contribution of growth data from possible late-time ISW or lensing effects in the CMB.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The suggestion to explicitly isolate the contribution of growth observables is well taken and will improve the robustness of our interpretation. We address the major comment below.

read point-by-point responses

  1. Referee: The central claim that the shift in neutrino-mass preference is driven by a degeneracy specifically in structure-growth observables (RSD and related data) is load-bearing for the interpretation. The manuscript should provide an explicit test (e.g., a run with RSD data removed) showing that the shift disappears or reverses when only CMB+BAO+SN are used, thereby isolating the contribution of growth data from possible late-time ISW or lensing effects in the CMB.

    Authors: We agree that an explicit test removing the RSD likelihood is the cleanest way to isolate the role of growth observables versus possible CMB contributions (late ISW or lensing). In the revised manuscript we will add a dedicated subsection and accompanying figure that repeats the full MCMC analysis using only CMB+BAO+SN. This will directly show whether the shift toward smaller (or negative) neutrino masses persists in the absence of RSD data. We expect the test to confirm that the degeneracy is driven by the growth observables, but we will report the outcome transparently regardless of the result. revision: yes

Circularity Check

0 steps flagged

No circularity: result obtained from external data fits

full rationale

The paper fits cosmological models to independent datasets (CMB, BAO, RSD, supernovae) both with and without dark-energy perturbations, then reports the resulting shifts in neutrino-mass posteriors. The claimed degeneracy is exhibited by comparing these fits rather than being imposed by definition, self-citation, or by relabeling a fitted parameter as a prediction. No load-bearing step reduces the reported neutrino-mass shift to an input by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis relies on standard cosmological modeling assumptions and data sets from prior literature; no new entities are postulated. Free parameters are the conventional ones in extended cosmological models.

free parameters (2)
  • dark energy equation-of-state parameters
    w0 and wa (or equivalent) in dynamical dark energy models, fitted to the data combinations.
  • sum of neutrino masses
    The primary parameter of interest, constrained via the joint fit.
axioms (2)
  • standard math Linear cosmological perturbation theory on an FLRW background
    Required to evolve dark energy and neutrino perturbations consistently.
  • domain assumption The chosen data sets (CMB, BAO, RSD, supernovae) provide independent constraints on the relevant parameters
    Invoked when combining the data to derive the neutrino mass shift.

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discussion (0)

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