  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 $N_{\nu}^{\rm eff}$.
