Massive Neutrinos in Cosmology

There are two places in cosmology where the mass of neutrinos would play a significant role. One is leptogenesis in the early universe, and the other is the evolution of mass density fluctuations that are explored with cosmic microwave background (CMB) fluctuations and the formation of cosmic structure. There is one more place where the presence of neutrinos is generally important — primordial nucleosynthesis, but the effect of neutrino mass is negligible unless it is unrealistically heavy. In this talk I discuss at some length the effect of the neutrino mass on the CMB fluctuations and cosmic structure formation, and the limit on the neutrino mass therefrom: we saw a substantial progress in our understanding after the reports of Wilkinson Microwave Anisotropy Probe (WMAP) [1] and Sloan Digital Sky Survey (SDSS) [2] but also some confusions still remain. We start with a brief mention about the status of leptogenesis.