Cosmological implications of light sterile neutrinos produced after the QCD phase transition

We study the production of sterile neutrinos in the early Universe from $\pi \to l{\nu }_s$ shortly after the QCD phase transition in the absence of a lepton asymmetry, while including finite-temperature corrections to the $\pi$ mass and decay constant $f_{\pi }$. Sterile neutrinos with masses $\lesssim 1\mathrm{MeV}$ produced via this mechanism freeze out at $T_f\simeq 10\mathrm{MeV}$ with a distribution function that is highly nonthermal and that features a sharp enhancement at low momentum, thereby making this species cold even for very light masses. Dark matter abundance constraints from the cosmic microwave background and phase space density constraints from the most dark-matter-dominated dwarf spheroidal galaxies provide upper and lower bounds, respectively, on combinations of mass and mixing angles. For $\pi \to \mu {\nu }_s$, the bounds lead to a narrow region of compatibility with the latest results from the 3.55-keV line. The nonthermal distribution function leads to free-streaming lengths (today) in the range of a few kpc, consistent with the observation of cores in dwarf galaxies. For sterile neutrinos with mass $\lesssim 1\mathrm{eV}$ that are produced by this reaction, the most recent accelerator and astrophysical bounds on $U_{ls}$ combined with the nonthermal distribution function suggests a substantial contribution from these sterile neutrinos to $N_{\text{eff}}$.

Figure 1

The gain/loss terms for the quantum kinetic equation describing ${\pi }^{+}\to \overline{\mu }{\nu }_{\mu }$.

Figure 2

Production rate of a sterile ${\nu }_s$ obtained from quantum kinetics from $\pi \to l{\nu }_s$ with $l=\mu ,e$. Note that for $m_{\nu }\lesssim 1\mathrm{MeV}$ the rate does not vary significantly.

Figure 3

Population buildup of a sterile ${\nu }_s$ obtained from quantum kinetics from $\pi \to l{\nu }_s$ with $l=\mu ,e$. Note that for $m_{\nu }\lesssim 1\mathrm{MeV}$ the buildup does not vary significantly.

Figure 4

Rates and population buildup of a sterile ${\nu }_s$ obtained from quantum kinetics from $\pi \to l{\nu }_s$ with $l=\mu ,e$, and $m_{{\nu }_s}$ near the kinematic threshold (for $\mu$ and $e$ production $m_{{\nu }_s}=30$ and 100 MeV, respectively).

Figure 5

The distribution function with various values of initial time. Note that an earlier initial time provides an enhancement with respect to later times.

Figure 6

The exact distribution function for small mass sterile neutrinos and an approximation keeping only the first term in the series expansion.

Figure 7

The bounds on sterile mass and mixing obtained from CMB and galactic measurements. The allowed regions determined from Eqs. (5.8) and (5.13) are shaded, and the sterile neutrino parameters that potentially explain the 3.5-keV signal (Bulbul et al.) are also shown.

Figure 8

Equation of state compared to thermal.