The late-time entropy production by massive particle decay induces various cosmological effects in the early epoch and modifies the standard scenario. We investigate the thermalization process of the neutrinos after entropy production by solving the Boltzmann equations numerically. We find that if the large entropy is produced at $t\sim 1\hspace{0.5em}\sec ,$ 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 ${}^4\mathrm{He},$ are drastically changed. Comparing with the observational light element abundances, we find that $T_R\lesssim 0.7\hspace{0.5em}\mathrm{MeV}$ 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., $T_R\gtrsim 2.5$–4 MeV, for the hadronic branching ratio $B_h{=10\mathrm{}}^{-2}-1.$ The 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 will be able to detect the vestige of the late-time entropy production as a modification of the effective number of the neutrino species $N_{\nu }^{\mathrm{eff}}.$

• Received 8 February 2000

DOI:https://doi.org/10.1103/PhysRevD.62.023506