MeV-scale Reheating Temperature and Thermalization of Neutrino   Background
  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 $N_{\nu}^{\rm eff}$. 
M. Kawasaki, K. Kohri and Naoshi Sugiyama