Thermalisation of light sterile neutrinos in the early universe

TL;DR

The paper tackles whether light sterile neutrinos thermalise before BBN by solving the full quantum kinetic equations for a 1 active + 1 sterile system. It systematically explores zero and sizable initial lepton asymmetries, across a grid of mass–mixing parameters, and quantifies thermalisation with $ ext{δN}_{ m eff}$ and $ ext{δN}_{ m eff,s}$. The key result is that full thermalisation is plausible at $L^{(a)}=0$ but can be heavily suppressed when $L^{(a)}=10^{-2}$ due to resonance blocking, implying that simple full-thermalisation assumptions are not generally justified. This has important implications for reconciling eV-scale sterile neutrinos with CMB/LSS and BBN constraints and highlights the need for more complete 3+1 analyses that include BBN effects.

Abstract

Recent cosmological data favour additional relativistic degrees of freedom beyond the three active neutrinos and photons, often referred to as 'dark' radiation. Light sterile neutrinos is one of the prime candidates for such additional radiation. However, constraints on sterile neutrinos based on the current cosmological data have been derived using simplified assumptions about thermalisation of the sterile neutrino at the Big Bang Nucleosynthesis (BBN) epoch. These assumptions are not necessarily justified and here we solve the full quantum kinetic equations in the (1 active + 1 sterile) scenario and derive the number of thermalised species just before BBN begins (T~1MeV) for null (L=0) and large (L=0.01) initial lepton asymmetry and for a range of possible mass-mixing parameters. We find that the full thermalisation assumption during the BBN epoch is justified for initial small lepton asymmetry only. Partial or null thermalisation occurs when the initial lepton asymmetry is large.

Figures (4)

• Figure 1: Iso-$\delta N_{\rm eff}$ contours in the $\sin^2 2\theta_s-\delta m_s^2$ plane for $L^{(\mu)}=0$ and $\delta m^2_s > 0$ (top panel) and $\delta m^2_s < 0$ (bottom panel). The green hexagon denotes the $\nu_s$ best-fit mixing parameters as in the $3+1$ global fit in Giunti:2011cp: $(\delta m^2_s,\sin^2 2\theta_s)=(0.9\ \text{eV}^2,0.089)$. The $1-2-3 \sigma$ contours denote the CMB+LSS allowed regions for $\nu_s$ with sub-eV mass as in Hamann:2010bk. In order to facilitate the comparison with the results presented in Sec \ref{['sec:largeleptona']}, a dashed rectangle denotes the parameter-space described by \ref{['zoomrange']}.
• Figure 2: Top panel: $\delta N_{\rm eff}$ as a function of the temperature for four different mixing angles ($\sin^2\ 2 \theta_s = 10^{-4}, 2 \times 10^{-3}, 5 \times 10^{-2}, 10^{-1}$) and fixed mass difference ($\delta m^2_s = 0.93\ \text{eV}^2$). Bottom panel: $\delta N_{\rm eff}$ as a function of the temperature for four different mass differences ($\delta m^2_s = 10^{-3}, 3.5 \times 10^{-2}, 9.3 \times 10^{-1}, 10$ eV$^2$) and fixed mixing angle ($\sin^2 2\theta_s = 0.051$). Thermalisation begins earlier and is more effective for larger mass differences and for larger mixing angles.
• Figure 3: Temperature evolution of active and sterile neutrino distributions for the resonant case $(\delta m^2_s,\sin^2 \theta_s)=(-3.3\ \text{eV}^2,6 \times 10^{-4})$ and $L^{(\mu)}=0$.
• Figure 4: Iso-$\delta N_{\rm eff}$ contours in the $\sin^2 2\theta_s-\delta m^2_s$ plane for $L^{(\mu)}=10^{-2}$ and $\delta m^2_s > 0$ (top panel) and $\delta m^2_s < 0$ (bottom panel), as in Fig. \ref{['fig:NHIH_zero']}.