The oscillation effects on thermalization of the neutrinos in the universe with low reheating temperature

TL;DR

This work investigates neutrino thermalization during MeV-scale reheating by solving momentum-dependent Boltzmann equations for neutrino density matrices, explicitly including flavor oscillations. It shows that oscillations reduce the electron-neutrino density, which can increase the neutron-to-proton freeze-out temperature and thus raise the $^4$He yield, even as the overall neutrino energy density (and thus $N_\nu$) may decrease. For $T_R$ around a few MeV, oscillations enhance $N_\nu$ by up to about 0.2 and significantly alter light-element abundances, leading to a tighter lower bound on the reheating temperature from BBN and cosmological data. The paper concludes that incorporating neutrino oscillations is crucial for correctly constraining the thermal history of the universe in low-$T_R$ scenarios, with a reference bound of $T_{RH} \gtrsim 2$ MeV (and $N_\nu \gtrsim 1.2$) when combining $^4$He and D observations.

Abstract

We study how the oscillations of the neutrinos affect their thermalization process during the reheating period with temperature O(1) MeV in the early universe. We follow the evolution of the neutrino density matrices and investigate how the predictions of big bang nucleosynthesis vary with the reheating temperature. For the reheating temperature of several MeV, we find that including the oscillations makes different predictions, especially for $^4$He abundance. Also, the effects on the lower bound of the reheating temperature from cosmological observations are discussed.

Figures (8)

• Figure 1: The final distribution functions of neutrinos. (a) and (c) are cases for no oscillations ($\nu_e$ is displayed by solid lines and $\nu_\mu$ by dashed lines) and (b) and (d) incorporate the oscillations ($\nu_e$ is displayed by solid lines, $\nu^\prime_\mu$ by dashed lines and $\nu^\prime_\tau$ by dot-dashed lines). The equilibrium distributions are drawn by dotted lines in order to show how much they are thermalized. For $T_R=15$ MeV, in (a) and (b), whether the oscillations are present or not, all the lines overlap and this means every neutrino species is fully thermalized for high reheating temperature. For $T_R=2.5$ MeV, in (c) and (d), distributions are away from equilibrium form. When the oscillations are taken into account, distributions of $\nu_e$ and $\nu^\prime_\mu$ get close as seen in (d).
• Figure 2: We draw the sums of the distribution functions, $f_{\nu_e}+f_{\nu_\mu}$ (no oscillation) and $f_{\nu_e}+f_{\nu^\prime_\mu}$ (including oscillation) with the dashed line and the solid line respectively. The latter is larger showing that the oscillations make the thermalization more efficient in total.
• Figure 3: The effective neutrino number $N_\nu$ as a function of the reheating temperature $T_R$ (shown on the bottom abscissa) or the decay width $\Gamma$ (shown on the top abscissa). The cases with and without the oscillations are drawn respectively by the solid and dashed lines. The horizontal line denotes $N_\nu=3.04$ with which $N_\nu$ for high $T_R$ should coincide (see the text).
• Figure 4: The $^4$He abundance (mass fraction) $Y_p$ as a function of the reheating temperature $T_R$ (shown on the bottom abscissa) or the decay width $\Gamma$ (shown on the top abscissa). The cases with and without the oscillations are drawn respectively by the solid and dashed curves. Thinner curves are calculated with fermi distributed neutrinos with $N_\nu$ of Fig. \ref{['fig:Nnu_compare']} (namely, only the change in the expansion rate due to the incomplete thermalization is taken into account). The horizontal line represents "standard " $Y_p$ calculated by BBN with neutrinos obeying the fermi distribution and $N_\nu=3.04$. The baryon-to-photon ratio is fixed at $\eta = 5 \times 10^{-10}$.
• Figure 5: The weak interaction rate $\Gamma_{n \rightarrow p}$ and the expansion rate $H$ as functions of temperature, where $\Gamma_{n \rightarrow p}$ and $H$ first become equal. We plot for $T_R = 2.5$ MeV with and without the oscillations. For $T_R=15$ MeV, the oscillations do not make any difference.