Cosmological preference for a positive neutrino mass at 2.7$\sigma$: A joint analysis of DESI DR2, DESY5, and DESY1 data

Technical Summary: Cosmological Preference for a Positive Neutrino Mass at 2.7σ

Problem Statement
While neutrino oscillation experiments have established that neutrinos possess non-zero masses, they cannot determine the absolute mass scale or the mass hierarchy (Normal vs. Inverted). Cosmological observations offer a sensitive probe for the total neutrino mass ($\sum m_\nu$), yet these constraints are highly dependent on the assumed cosmological model, particularly the nature of dark energy (DE). Previous systematic studies by the authors indicated a degeneracy where specific dynamical DE behaviors—specifically an equation of state (EoS) evolving from $w < -1$ at early times to $w > -1$ at late times—could relax upper limits on $\sum m_\nu$ compared to the standard $\Lambda$CDM model. Recent data from the Dark Energy Spectroscopic Instrument (DESI) DR2 suggests a statistically significant preference for such dynamical DE behavior, potentially creating an environment where a positive neutrino mass can be measured with higher confidence.

Methodology
The authors perform a joint Markov Chain Monte Carlo (MCMC) analysis using the Cobaya sampler and CAMB code to constrain cosmological parameters. The analysis incorporates a comprehensive dataset:

• CMB: Planck 2018 temperature and polarization spectra, NPIPE PR4 lensing reconstruction, and ACT DR6.
• DESI: Baryon Acoustic Oscillation (BAO) measurements from the second data release (DR2).
• Supernovae (SN): DESY5 (photometric) and PantheonPlus (spectroscopic) samples.
• Weak Lensing: DESY1 data covering 26 million source galaxies.

The study compares three cosmological frameworks, all extended to include the total neutrino mass ($\sum m_\nu$) and the effective number of relativistic species ($N_{\text{eff}}$) as free parameters:

1. $\Lambda$CDM + $\sum m_\nu$ + $N_{\text{eff}}$: Standard model with a cosmological constant.
2. $w$CDM + $\sum m_\nu$ + $N_{\text{eff}}$: Model with a constant dark energy EoS ($w$).
3. $w_0w_a$CDM + $\sum m_\nu$ + $N_{\text{eff}}$: Model with a dynamical DE EoS parameterized by the Chevallier-Polarski-Linder (CPL) form, $w(a) = w_0 + w_a(1-a)$.

Flat priors are applied to all parameters, with specific attention to the interplay between DE dynamics and neutrino properties.

Key Contributions and Results
The primary result is a high-confidence measurement of a non-zero, positive neutrino mass within the dynamical DE framework.

• Main Finding: In the $w_0w_a$CDM + $\sum m_\nu$ + $N_{\text{eff}}$ model, the joint analysis of CMB, DESI DR2, DESY5, and DESY1 data yields a total neutrino mass of:
  $$\sum m_\nu = 0.098^{+0.016}_{-0.037} \text{ eV}$$
  This represents a 2.7$\sigma$ detection of a positive neutrino mass.

• Model Dependence:

  • In the $\Lambda$CDM and $w$CDM frameworks, the analysis only yields upper limits (e.g., $\sum m_\nu < 0.085$ eV in $\Lambda$CDM with all data).
  • Replacing the DESY5 supernova data with PantheonPlus weakens the evidence for dynamical DE (dropping to $\sim$2$\sigma$) and reverts the neutrino mass result to an upper limit ($\sum m_\nu < 0.144$ eV), demonstrating the sensitivity of the result to the specific supernova dataset and the strength of the DE dynamical signal.

• Drivers of the Result: The paper identifies three specific factors driving the 2.7$\sigma$ preference for a positive mass:

  1. DESI's Preference for Dynamical DE: The data favor an EoS evolving from $w < -1$ (early times) to $w > -1$ (late times). This specific evolution increases the late-time expansion rate relative to $\Lambda$CDM in a way that requires a larger $\sum m_\nu$ to maintain consistency with CMB acoustic peak constraints (specifically the angular diameter distance to last scattering).
  2. Free $N_{\text{eff}}$: The analysis finds a best-fit $N_{\text{eff}} = 2.46^{+0.60}_{-0.24}$, which is lower than the standard model value (3.044). A reduced $N_{\text{eff}}$ implies a lower neutrino number density, necessitating a larger total mass to produce equivalent late-time effects on structure formation and background expansion.
  3. Weak Lensing (DESY1): The inclusion of DESY1 data, which prefers a lower clustering amplitude ($S_8$), suppresses the lower-mass peak in the posterior distribution, further supporting a non-zero mass.

• Physical Interpretation: The authors analyze the relative expansion rate $E(z)$, showing that the dynamical DE behavior (crossing $w=-1$) creates a geometric integral deviation. To compensate for this while keeping the CMB acoustic peak positions fixed, the model naturally increases $\sum m_\nu$. This mechanism aligns with the authors' previous theoretical work on parameter degeneracies.

Significance
The paper claims that this result marks a new era in cosmological neutrino mass measurement, driven by the DESI dataset. The 2.7$\sigma$ detection of a positive mass is consistent with the lower bounds of the Normal Hierarchy ($\sum m_\nu \gtrsim 0.06$ eV) but does not support the Inverted Hierarchy, aligning with current particle physics constraints. The authors emphasize that the robustness of this detection is intrinsically linked to the evidence for dynamical dark energy; as future DESI data releases potentially strengthen the preference for dynamical DE, the confidence in a non-zero neutrino mass measurement is expected to increase. The work underscores the necessity of considering dynamical DE and varying $N_{\text{eff}}$ simultaneously to avoid artificially tightening constraints on neutrino mass.