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 to accept a theoretical prediction , \Omega _ { b } h ^ { 2 } \leq 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 \geq 10 M _ { \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 .

KEYWORDS : Big-Bang cosmology , supernovae , explosive nucleosynthesis