MeV-scale Reheating Temperature and Thermalization of Neutrino Background

TL;DR

The study addresses how late-time entropy production from decays of massive particles affects neutrino thermalization, BBN yields, and cosmological observables. It uses a numerical Boltzmann framework to track neutrino distributions, defines the reheating temperature $T_R$ through $\,\Gamma=3H(T_R)$ with $H$ given by $H=\sqrt{g_*\pi^2/90}\,\frac{T_R^2}{M_G}$, and includes hadron-injection effects via hadronic branching $B_h$ and jet yields. It finds that $T_R \lesssim 0.7$ MeV is excluded at 95% C.L. in the absence of hadronic decays, with $N_\nu^{\rm eff}$ potentially as low as ~0.1 in extreme cases; when hadrons are injected, the bound strengthens to $T_R \gtrsim 2.5$–$4$ MeV and $N_\nu^{\rm eff}$ can be ~1.9–2.8. The results imply observable consequences for large-scale structure and CMB anisotropies, and future MAP/Planck data could detect or constrain such late-time entropy production, thereby informing SUSY/thermal inflation scenarios.

Abstract

The late-time entropy production by the massive particle decay induces the various cosmological effects in the early epoch and modify the standard scenario. We investigate the thermalization process of the neutrinos after the entropy production by solving the Boltzmann equations numerically. We find that if the large entropy are produced at t $\sim$ 1 sec, the neutrinos are not thermalized very well and do not have the perfect Fermi-Dirac distribution. Then the freeze-out value of the neutron to proton ratio is altered considerably and the produced light elements, especially He4, are drastically changed. Comparing with the observational light element abundances, we find that $T_R$ < 0.7 MeV is excluded at 95 % C.L. We also study the case in which the massive particle has a decay mode into hadrons. Then we find that $T_R$ should be a little higher, i.e. $T_R$ > 2.5 MeV - 4 MeV, for the hadronic branching ratio $B_h = 10^{-2} - 1$. Possible influence of late-time entropy production on the large scale structure formation and temperature anisotropies of cosmic microwave background is studied. It is expected that the future satellite experiments (MAP and PLANCK) to measure anisotropies of cosmic microwave background radiation temperature can detect the vestige of the late-time entropy production as a modification of the effective number of the neutrino species $N_ν^{\rm eff}$.

Figures (17)

• Figure 1: Time evolution of the cosmic temperature (a) for $T_{R}=10$ MeV, and (b) for $T_{R}=2$ MeV. The dashed line denotes the neutrino temperature which can be defined only when they are thermalized sufficiently and have the perfect Fermi-Dirac distribution.
• Figure 2: Time evolution of the fraction of the energy density of $\nu_{e}$ (solid curve) and $\nu_{\mu}$ (dashed curve) to that of the standard big bang scenario for (a) $T_{R}= 10$ MeV and (b)$T_{R}=2$ MeV. Since the interaction of $\nu_{\tau}$ is as same as $\nu_{\mu}$, the curve of $\nu_{\mu}$ also represents $\nu_{\tau}$.
• Figure 3: Distribution function of $\nu_{e}$ (solid curve) and $\nu_{\mu}$ (dashed curve) (a)for $T_{R}=10$ MeV and (b)for $T_{R}=2$ MeV. The dotted curve is the Fermi-Dirac distribution function. Since the interaction of $\nu_{\tau}$ is as same as $\nu_{\mu}$, the curve of $\nu_{\mu}$ also represents $\nu_{\tau}$.
• Figure 4: Effective number of neutrino species $N_{\nu}^{\rm eff}$ as a function of reheating temperature $T_{R}$. The top horizontal axis denotes the lifetime which corresponds to $T_{R}$.
• Figure 5: Weak interaction rates (sec$^{-1}$) between neutron and proton. The upper curves are $\Gamma_{n \rightarrow p}$. The lower curves are $\Gamma_{p \rightarrow n}$. The solid lines denote the case of $T_R = 10$ MeV which corresponds to the standard big bang scenario. The dotted lines denote the case of $T_R = 1$ MeV in the late-time entropy production scenario. Notice that $\Gamma_{n \rightarrow p}^{-1}$ reaches $\tau_n = 887$ sec in the low temperature.