Are Cosmological Data Excluding Sterile Neutrinos or Only the Fully Thermalized Limit?

Technical Summary: Cosmological Data Excluding Sterile Neutrinos or Only the Fully Thermalized Limit?

Problem Statement
The standard cosmological model ($\Lambda$CDM) successfully describes the Universe but leaves fundamental questions regarding the neutrino sector unanswered. While terrestrial experiments (e.g., KATRIN, MicroBooNE) have tightened constraints on light sterile neutrinos, they have not entirely excluded them. In cosmology, the viability of sterile neutrinos depends not only on their physical mass ($m_s$) but critically on their production history and phase-space distribution. Previous analyses have largely focused on the "fully thermalized" limit, where sterile neutrinos are assumed to be in thermal equilibrium with active neutrinos, contributing $\Delta N_{\text{eff}} \simeq 1$. This specific scenario is strongly disfavored by current data. However, it remains unclear whether cosmological observations generically exclude the entire class of sterile neutrinos or merely the specific assumption of full thermalization. This paper addresses whether current data exclude sterile neutrinos as a general physical category or primarily the fully populated thermal limit.

Methodology
The authors perform a systematic reassessment of light sterile-neutrino scenarios using a consistent statistical pipeline across different cosmological backgrounds and production mechanisms.

• Scenarios Considered: Three distinct realizations of a light massive sterile species are analyzed:

  1. Fully Thermalized Sterile (FTS): The sterile state follows a standard Fermi-Dirac distribution with the same temperature as active neutrinos ($T_s = T_\nu$), yielding $\Delta N_{\text{eff}} \simeq 1$ and an effective mass $m_s^{\text{eff}} = m_s$.
  2. Thermal Relic with Different Temperature (DTS): The sterile state follows a Fermi-Dirac distribution but with a suppressed temperature ($T_s < T_\nu$). Here, $\Delta N_{\text{eff}} = (T_s/T_\nu)^4$ and $m_s^{\text{eff}} = m_s (\Delta N_{\text{eff}})^{3/4}$.
  3. Dodelson–Widrow-like (DW): The sterile state is produced out of equilibrium via active-sterile oscillations, retaining the thermal shape but with a suppressed normalization factor $\chi$. Here, $\Delta N_{\text{eff}} = \chi$ and $m_s^{\text{eff}} = \chi m_s$.

• Cosmological Frameworks: Analyses are conducted within both the standard $\Lambda$CDM model and the Chevallier–Polarski–Linder (CPL) dynamical dark-energy model ($w(a) = w_0 + w_a(1-a)$).

• Datasets: The study combines:

  • Planck 2018 CMB: Temperature, polarization, and lensing data.
  • DESI DR2 BAO: Baryon Acoustic Oscillation measurements from galaxy and quasar tracers and the Lyman-$\alpha$ forest.
  • Type Ia Supernovae (SNIa): PantheonPlus and Union3 compilations.
  • Local $H_0$ Prior: A Gaussian prior ($H_0 = 73.5 \pm 0.81$ km s$^{-1}$ Mpc$^{-1}$) is applied in specific reweighting analyses to test the Hubble tension resolution.

• Statistical Approach: Parameter constraints are derived using Markov Chain Monte Carlo (MCMC) via MontePython and the Boltzmann solver CLASS. Model comparison utilizes the minimum chi-square ($\chi^2_{\text{min}}$), the Akaike Information Criterion (AIC), and Bayesian evidence (Bayes factors) to assess statistical preference relative to baseline models without sterile components.

Key Results

1. Fully Thermalized Scenario (FTS):

   • In baseline analyses (without the local $H_0$ prior), the FTS scenario is strongly disfavored in both $\Lambda$CDM and CPL frameworks. The degradation in fit is significant ($\Delta \chi^2_{\text{min}} \approx 30\text{--}40$), and Bayesian evidence strongly rejects the model ($\Delta \ln B \approx -18 \text{ to } -22$).
   • The FTS model drives the inferred $H_0$ to $\approx 73.5$ km s$^{-1}$ Mpc$^{-1}$, alleviating the Hubble tension, but at the cost of a poor fit to CMB and BAO data.
   • When the local $H_0$ prior is included via importance reweighting, the $\Lambda$CDM+FTS model becomes statistically competitive with standard $\Lambda$CDM (Bayes factors become inconclusive or weakly negative). However, the sterile mass remains consistent with zero; the improvement stems from the relativistic energy density, not a massive sterile state.

2. Thermal Relic with Suppressed Temperature (DTS):

   • This scenario is broadly compatible with observations. The fit degradation is minimal ($\Delta \chi^2_{\text{min}} \approx -0.5 \text{ to } +1.0$).
   • Bayesian evidence shows that DTS is not decisively excluded and, in some combinations (e.g., CPL + Union3), exhibits a mild preference over the baseline.
   • Constraints on the effective abundance are tight ($\Delta N_{\text{eff}}^{\text{sterile}} \lesssim 0.03\text{--}0.09$), but the physical mass $m_s$ is weakly constrained (up to $\sim 4.7$ eV) because the colder temperature suppresses the cosmological impact.

3. Dodelson–Widrow-like Scenario (DW):

   • The DW scenario is moderately disfavored but significantly more viable than FTS. The Bayesian penalty is weak-to-moderate ($\Delta \ln B \approx -1.8 \text{ to } -3.8$).
   • Constraints on $\Delta N_{\text{eff}}^{\text{sterile}}$ are weaker than in DTS ($\lesssim 0.24\text{--}0.31$) due to the different prior structure (sampling $\chi$ directly), but the effective mass remains tightly constrained ($m_s^{\text{eff}} \lesssim 0.03\text{--}0.11$ eV).
   • The DW scenario allows for a modest increase in $H_0$ ($\approx 69$ km s$^{-1}$ Mpc$^{-1}$ in $\Lambda$CDM) but does not resolve the Hubble tension as effectively as FTS.

4. Global Hierarchy:

   • The Bayesian evidence establishes a clear hierarchy of viability: FTS $\ll$ DW < DTS.
   • The DTS scenario yields the weakest cosmological pressure, followed by DW, while FTS is decisively excluded in baseline analyses.

Significance and Conclusions
The paper concludes that current cosmological data do not generically exclude sterile neutrinos as a class. Instead, the strong exclusion applies specifically to the assumption of full thermalization (maximal abundance and $\Delta N_{\text{eff}} \simeq 1$).

• Production History Matters: The cosmological impact of a sterile neutrino is determined by the interplay between its physical mass and its phase-space distribution (abundance and temperature). Scenarios with suppressed populations (DTS and DW) can evade the tight constraints that rule out the fully thermalized limit.
• Interpretation of Constraints: Claims that "cosmology excludes sterile neutrinos" are accurate only when referring to the fully thermalized benchmark. More general, partially populated realizations remain consistent with current observations.
• Future Implications: The results highlight that robust conclusions regarding sterile neutrinos require careful consideration of the specific microphysical production mechanism and thermal history. Future cosmological surveys will need to distinguish between these different production histories to definitively test the existence of sterile neutrinos.

The authors emphasize that while the fully thermalized limit is strongly disfavored, the door remains open for sterile neutrinos with suppressed abundances, particularly those with colder thermal distributions or reduced normalization.