Cosmological Nucleosynthesis in the Big-Bang and Supernovae

Recent observation of the power spectrum of Cosmic Microwave Background (CMB) Radiation has exhibited that the flat cosmology is most likely. This suggests too large universal baryon-density parameter $\Omega_b h^2 \approx 0.022 \sim 0.030$toacceptatheoreticalprediction,$\Omega_b h^2 \le 0.017$, in the homogeneous Big-Bang model for primordial nucleosynthesis. Theoretical upper limit arises from the sever constraints on the primordial ${}^7$Li abundance. We propose two cosmological models in order to resolve the descrepancy; lepton asymmetric Big-Bang nucleosynthesis model, and baryon inhomogeneous Big-Bang nucleosynthesis model. In these cosmological models the nuclear processes are similar to those of the r-process nucleosynthesis in gravitational collapse supernova explosions. Massive stars $\ge 10M_{\odot }$ culminate their evolution by supernova explosions which are presumed to be the most viable candidate site for the r-process nucleosynthesis. Even in the nucleosynthesis of heavy elements, initial entropy and density at the surface of proto-neutron stars are so high that nuclear statistical equilibrium favors production of abundant light nuclei. In such explosive circumstances many neutron-rich radioactive nuclei of light-to-intermediate mass as well as heavy mass nuclei play the significant roles.