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Negative neutrino mass or negative dark energy?

This paper proposes that a sign-switching cosmological constant model ( $\Lambda_\mathrm{s}$ CDM) can resolve the tension between cosmological data and neutrino oscillation experiments by modifying the late-time expansion history, thereby shifting the inferred effective neutrino mass from a negative value to a physically consistent positive range.

Original authors: Cihad Kıbrıs, Willem Elbers, Özgür Akarsu, Eleonora Di Valentino

Published 2026-05-21

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CC BY 4.0

Original authors: Cihad Kıbrıs, Willem Elbers, Özgür Akarsu, Eleonora Di Valentino

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: The Universe's "Negative Weight"

Imagine the universe as a giant, expanding balloon. Scientists have been measuring how fast this balloon is inflating and how heavy the stuff inside it is. They use two main tools:

DESI (The Ruler): Measures distances to galaxies nearby (low redshift).
CMB (The Baby Photo): Looks at the oldest light in the universe to see how it was shaped when the universe was a baby.

For a long time, scientists used a standard recipe called $\Lambda$ CDM (Lambda-Cold Dark Matter) to explain how the universe works. But recently, when they combined the "Ruler" data with the "Baby Photo" data, the recipe broke.

The math suggested that the total weight of neutrinos (tiny, ghostly particles that fly through everything) had to be negative.

Why is this weird?
Think of neutrinos like sand in an hourglass. You can have a lot of sand, a little sand, or no sand. But you cannot have "negative sand." If the math says you have negative sand, it means the recipe (the model) is missing a crucial ingredient. The universe isn't actually made of negative mass; the model is just struggling to fit the data.

The Solution: Trying Different "Dark Energy" Recipes

The authors asked: If the universe doesn't have negative neutrino mass, what else could be causing this weird math?

They hypothesized that the problem isn't the neutrinos, but Dark Energy (the mysterious force pushing the universe apart). They tested several new recipes for Dark Energy to see if any of them could fix the math without needing "negative sand."

Think of Dark Energy as the gas pedal of the universe.

Standard Recipe ( $\Lambda$ CDM): The gas pedal is stuck at a constant, steady pressure.
The Problem: The data says the universe expanded too slowly in the middle of its life (when the "Baby Photo" was taken) but too fast recently (when the "Ruler" was measured). A constant gas pedal can't explain this.

The authors tested three main types of new gas pedals:

1. The "Magic Switch" ( $\Lambda_s$ CDM)

This is the star of the show. Imagine the gas pedal has a secret switch.

In the past (High Redshift): The switch flips the pedal to negative pressure (like a brake or a vacuum). This slows the universe down just enough to match the "Baby Photo."
In the recent past (Low Redshift): The switch flips back to positive pressure (a normal gas pedal). This speeds the universe up to match the "Ruler" measurements.

The Result: This "Magic Switch" model worked perfectly. When they used this model, the math stopped asking for "negative neutrino mass." Instead, it said the neutrinos have a normal, positive weight (about 0.055 eV), which fits with what we know from particle physics experiments on Earth.

2. The "Shape-Shifter" (Omnipotent Dark Energy)

This model tries to change the gas pedal's pressure in a complex, wavy way. It can go negative and positive, but it's a bit messy.

The Result: It helped a little, but it didn't fix the problem as cleanly as the "Magic Switch." The math still hinted at slightly negative neutrino mass, just not as badly as before.

3. The "Standard Variations" (CPL, Mirage, etc.)

These are models where the gas pedal changes pressure smoothly but never goes negative. It just gets weaker or stronger.

The Result: These models couldn't fix the problem. They couldn't create the specific "braking" effect needed in the middle of the universe's history. The math still demanded "negative neutrino mass."

4. The "Curved Room" ( $\Lambda$ CDM + Curvature)

This model suggests the universe isn't flat like a sheet of paper, but curved like a sphere or a saddle.

The Result: Even if the universe is curved, the data from the "Ruler" and "Baby Photo" are so precise that this curvature can't fix the neutrino problem. The math still demands negative mass.

The Main Takeaway

The paper concludes that the "negative neutrino mass" isn't a real thing. It's a symptom.

The Symptom: The standard model is missing a specific type of "braking" mechanism in the universe's history.
The Cure: The best cure found so far is the "Magic Switch" ( $\Lambda_s$ CDM). This model suggests that at a specific time in the past (around 2.4 billion years ago, or redshift $z > 2.4$ ), the vacuum energy of the universe briefly flipped signs, acting like a temporary brake before switching back to pushing the universe apart.

Summary in a Nutshell

The universe is acting like a car that suddenly slowed down in the middle of a trip and then sped up again. The standard map (model) says the car must have had "negative weight" to do this. The authors found a new map that says, "No, the car just had a special engine that hit the brakes and then the gas."

This new engine (the sign-switching cosmological constant) explains the data perfectly and lets the neutrinos keep their normal, positive weight. While this new model isn't the statistically perfect winner in every single test, it is the only one that makes physical sense of the "negative mass" mystery.

Technical Summary: Negative Neutrino Mass or Negative Dark Energy?

Problem Statement
Recent cosmological analyses combining Dark Energy Spectroscopic Instrument (DESI) Baryon Acoustic Oscillation (BAO) data with Cosmic Microwave Background (CMB) observations have revealed a significant tension within the standard $\Lambda$ CDM model. When the sum of neutrino masses ( $\sum m_\nu$ ) is treated as a free parameter, the data prefer a value that falls below the robust lower limit established by neutrino oscillation experiments ( $\sum m_\nu \geq 0.059$ eV). Specifically, allowing the effective neutrino mass parameter ( $\sum m_{\nu, \text{eff}}$ ) to explore unphysical negative values results in a posterior distribution peaking in the negative region (e.g., $\sum m_{\nu, \text{eff}} \approx -0.075$ eV at 68% confidence). This "neutrino mass tension" suggests a mismatch between low-redshift distance measurements (DESI BAO) and the CMB lensing amplitude, which the standard model cannot resolve without invoking unphysical parameters. The authors posit that this preference for negative mass is a diagnostic signal indicating a missing negative effective contribution to the late-time expansion history, rather than evidence for negative rest masses.

Methodology
The authors perform a systematic Bayesian analysis using the Cobaya package and a modified version of the Boltzmann solver CLASS. They compare the standard $\Lambda$ CDM model against a suite of alternative dark energy (DE) and geometric models, all extended to allow $\sum m_{\nu, \text{eff}}$ to vary freely (including negative values). The data sets include:

DESI DR2 BAO: Measurements of $D_M(z)/r_d$ and $D_H(z)/r_d$ over $0.4 < z < 4.2$ .
CMB: Planck and ACT temperature/polarization data, combined with CMB lensing reconstruction from Planck, ACT, and SPT-3G.
Supernovae: The DES-Dovekie Type Ia supernova sample.

The study categorizes models into three classes to test different mechanisms for alleviating the tension:

Density-level models with sign-switching:
- $\Lambda_s$ CDM: A sign-switching cosmological constant where the vacuum energy is negative (AdS-like) for $z > z^\dagger$ and positive (dS-like) for $z < z^\dagger$ .
- Omnipotent Dark Energy (ODE/DMS20): A model allowing non-monotonic density evolution that can access a negative-density branch.
Equation-of-State (EoS) based models (sign-preserving density):
- CPL ( $w_0 w_a$ CDM): Standard dynamical DE with $w_{DE}(a) = w_0 + w_a(1-a)$ .
- Mirage DE: A specific trajectory in the CPL parameter space.
- NPDDE: Non-phantom dynamical dark energy ( $w_{DE} \geq -1$ ).
- $w$ CDM: Constant equation of state.
Geometric extension:
- $\Lambda$ CDM+ $\Omega_k$ : Allowing for spatial curvature.

The analysis evaluates models based on two criteria: statistical improvement (Bayesian evidence and $\chi^2$ ) and physical mechanism (whether the model explicitly supplies the required negative contribution to the expansion history to replace the role of $\sum m_{\nu, \text{eff}} < 0$ ).

Key Contributions and Results
The paper establishes a hierarchy of model performance in resolving the neutrino mass tension:

Baseline Tension: In the free- $\sum m_{\nu, \text{eff}}$ $\Lambda$ CDM model, the posterior peaks at $\sum m_{\nu, \text{eff}} = -0.090^{+0.040}_{-0.050}$ eV (DESI + CMB), confirming the anomaly.
$\Lambda_s$ CDM Success: The sign-switching cosmological constant model is uniquely capable of recovering a physically consistent positive neutrino mass.
- For DESI + CMB: $\sum m_{\nu, \text{eff}} = 0.040 \pm 0.051$ eV.
- For DESI + CMB + DES-Dovekie SNe: $\sum m_{\nu, \text{eff}} = 0.055 \pm 0.050$ eV.
- The model constrains the transition redshift to $z^\dagger > 2.4$ (95% CL).
- Mechanism: $\Lambda_s$ CDM suppresses the expansion rate $H(z)$ at intermediate redshifts ( $z \gtrsim 2$ ) via the negative AdS-like branch, enhancing structure growth and CMB lensing. It then restores a higher expansion rate at lower redshifts to match DESI BAO distances. This specific redshift-structured deformation mimics the effect of a negative neutrino mass without requiring unphysical parameters.
ODE/DMS20 Performance: While ODE has the structural capacity to access negative densities, the posterior distribution does not concentrate in the regions where this branch acts as a clean replacement for $\sum m_{\nu, \text{eff}} < 0$ . The marginalized result remains near or slightly below zero ( $\sum m_{\nu, \text{eff}} \approx -0.04$ eV).
EoS-based Models: Models with sign-preserving densities (CPL, Mirage, NPDDE) can soften the anomaly by broadening degeneracies but fail to decisively shift the mass to the positive region. Mirage DE is the closest competitor among EoS models, yielding a mildly positive mass ( $\sim 0.017$ eV) when supernovae are included, but it lacks the explicit negative-density branch.
Spatial Curvature: The $\Lambda$ CDM+ $\Omega_k$ model fails to resolve the tension. Even with $\Omega_k < 0$ (closed universe), which provides a negative geometric contribution, the data favor $\Omega_k \approx 0$ , and the inferred neutrino mass remains negative ( $\sum m_{\nu, \text{eff}} \approx -0.12$ eV).

Significance and Claims
The authors claim that the preference for negative effective neutrino masses should not be viewed merely as a statistical fluctuation or a pathology to be removed by priors, but as a diagnostic of missing late-time cosmological structure.

Specific Mechanism Required: The data do not simply require "more freedom" in the dark energy sector. Instead, they point toward a specific sign- and redshift-structured deformation of the expansion history: a suppression of $H(z)$ over the intermediate-redshift range relevant for CMB lensing ( $1.5 \lesssim z \lesssim 10$ ), followed by a restoration of a larger expansion rate at lower redshifts.
$\Lambda_s$ CDM as a Benchmark: While $\Lambda_s$ CDM is not the global statistical winner in terms of Bayesian evidence (due to parameter volume penalties), it is identified as the cleanest mechanism-level realization of the required physics among the models tested. It directly translates the phenomenological need for a negative contribution into a concrete, negative vacuum-energy branch.
Modest Conclusion: The paper does not claim that $\Lambda_s$ CDM is definitively the correct theory of the universe, nor that the current data uniquely require a sign-switching cosmological constant. Rather, it argues that if the neutrino mass tension is physical, the solution must involve a late-time sector with the specific sign and redshift structure provided by $\Lambda_s$ CDM. The tension serves as a guide to the type of new physics (a negative effective contribution to the Friedmann equation) required to reconcile DESI BAO distances with CMB lensing.