Heavy sterile neutrinos, entropy and relativistic energy production, and the relic neutrino background

Abstract

We explore the implications of the existence of heavy neutral fermions (i.e., sterile neutrinos) for the thermal history of the early universe. In particular, we consider sterile neutrinos with rest masses in the 100 MeV to 500 MeV range, with couplings to ordinary active neutrinos large enough to guarantee thermal and chemical equilibrium at epochs in the early universe with temperatures T > 1 GeV, but in a range to give decay lifetimes from seconds to minutes. Such neutrinos would decouple early, with relic densities comparable to those of photons, but decay out of equilibrium, with consequent prodigious entropy generation prior to, or during, Big Bang Nucleosynthesis (BBN). Most of the ranges of sterile neutrino rest mass and lifetime considered are at odds with Cosmic Microwave Background (CMB) limits on the relativistic particle contribution to energy density (e.g., as parameterized by N_eff). However, some sterile neutrino parameters can lead to an acceptable N_eff. These parameter ranges are accompanied by considerable dilution of the ordinary background relic neutrinos, possibly an adverse effect on BBN, but sometimes fall in a range which can explain measured neutrino masses in some particle physics models. A robust signature of these sterile neutrinos would be a measured N_eff not equal to 3 coupled with no cosmological signal for neutrino rest mass when the detection thresholds for these probes are below laboratory-established neutrino mass values, either as established by the atmospheric neutrino oscillation scale or direct measurements with, e.g., KATRIN or neutrino-less double beta decay experiments.

Figures (12)

• Figure 1: Branching ratios for selected decay processes and the branching ratio-weighted fraction of sterile neutrino rest mass (neglecting thermalization) deposited in the decoupled active neutrino seas are shown as functions of sterile neutrino rest mass in MeV.
• Figure 2: Contours of sterile neutrino lifetime $\tau$ in seconds as functions of sterile neutrino rest mass $m_s$ and $\sin^22\theta$.
• Figure 3: Same as Fig. \ref{['tau']}, but for lower ranges of sterile neutrino rest mass and larger vacuum mixing angles.
• Figure 4: Temperature versus decoupled active neutrino temperature for several scenarios as labeled. The decoupled active neutrino temperature (dashed line), decreasing to the left here, is inversely proportional to scale factor, which therefore increases to the right. The dash-dot-dot (blue) line shows the standard expansion with no sterile neutrinos, exhibiting the transfer of entropy from electron/positron pairs to photons as the former annihilate. The lighter solid (red) curve shows what happens in a scenario with a sterile neutrino with rest mass $m_s=275\,{\rm MeV}$ and lifetime $\tau=100\,{\rm s}$.
• Figure 5: Entropy-per-baryon (in units of Boltzmann's constant $k_{\rm b}$) versus photon (plasma) temperature for the standard cosmology case (constant co-moving entropy, dashed line) and for a scenario with a sterile neutrino with rest mass $m_s=275\,{\rm MeV}$ and lifetime $\tau=100\,{\rm s}$ (solid line). Beginning and ending entropy-per-baryon for the latter case as indicated.