Sterile Neutrino Hot, Warm, and Cold Dark Matter

TL;DR

The paper investigates the production of sterile neutrino dark matter in the early universe through both non-resonant and resonant scattering processes, spanning hot, warm, and cold dark matter phenomenology. It develops a comprehensive, temperature-, density-, and damping-aware Boltzmann framework that includes finite-temperature effects, lepton asymmetries, and QCD-transition dilution to predict relic densities and spectra as functions of sterile-neutrino mass $m_s$ and mixing $\sin^2 2\theta$, with $\Omega_{ν_s} h^2$ approximately scaling as $0.3\,(\sin^2 2\theta/10^{-10})(m_s/100\,\mathrm{keV})^2$ in the nonresonant case. The work then maps cosmological and astrophysical constraints from DEBRA, CMB, BBN, and Li-6/D photoproduction, as well as core-collapse supernova energy-loss considerations, to carve out viable regions of parameter space and discuss implications for structure formation and potential X-ray signatures from radiative decays. The findings show that sterile neutrinos can viably constitute all dark matter across broad ranges of $m_s$ and $\theta$, producing diverse velocity distributions and enabling both warm and cold dark matter behavior, while remaining consistent with current observations. This provides a compelling, testable alternative to WIMPs and links particle physics models of sterile states to observable cosmological and astrophysical phenomena, including possible detections via X-ray observations and precise CMB measurements.

Abstract

We calculate the incoherent resonant and non-resonant scattering production of sterile neutrinos in the early universe. We find ranges of sterile neutrino masses, vacuum mixing angles, and initial lepton numbers which allow these species to constitute viable hot, warm, and cold dark matter (HDM, WDM, CDM) candidates which meet observational constraints. The constraints considered here include energy loss in core collapse supernovae, energy density limits at big bang nucleosynthesis, and those stemming from sterile neutrino decay: limits from observed cosmic microwave background anisotropies, diffuse extragalactic background radiation, and Li-6/D overproduction. Our calculations explicitly include matter effects, both effective mixing angle suppression and enhancement (MSW resonance), as well as quantum damping. We for the first time properly include all finite temperature effects, dilution resulting from the annihilation or disappearance of relativistic degrees of freedom, and the scattering-rate-enhancing effects of particle-antiparticle pairs (muons, tauons, quarks) at high temperature in the early universe.

Figures (8)

• Figure 1: An example of the temperature evolution of the active and sterile neutrino effective mass-squared, $m^2_{\rm eff}$. The active neutrino $m^2_{\rm eff}$ is dominated by a positive finite density potential at lower temperatures and turns over when the thermal potential dominates. Resonance occurs at level crossings, where the active and sterile $m^2_{\rm eff}$ tracks intersect.
• Figure 2: Regions of $\Omega_{\nu_s} h^2$ produced by resonant and nonresonant $\nu_e \leftrightarrow \nu_s$ neutrino conversions for selected net lepton number $L$, after applying all constraints (see Secs. \ref{['cosmoconstraints']} and \ref{['supernovaconstraints']}). Regions of parameter space disfavored by supernova core collapse considerations are shown with vertical stripes.
• Figure 3: Same as Fig. \ref{['omegaepanel']}, but for $\nu_\tau \leftrightarrow \nu_s$.
• Figure 4: The effective matter mixing $\sin^2 2\theta_m$ is shown for a case with two resonances (solid line). For this case, $m_s = 1\,\rm keV$, $\sin^2 2\theta = 10^{-9}$, $L = 6 \times 10^{-4}$, and $T = 130\,\rm MeV$. The dashed line is the active neutrino energy distribution.
• Figure 5: The sterile neutrino distribution for four cases of resonant and non-resonant $\nu_e \leftrightarrow \nu_s$, as described in the text. The dotted line is a normalized active neutrino spectrum. The thick-solid, dashed, dot-dashed, and thin-solid lines correspond to cases (1)--(4), respectively. The inset shows a magnified view of the low momenta range of the distributions.