Universal baryon‐density parameter &OHgr;Binferred from the Big‐Bang nucleosynthesis and cosmic microwave background fluctuations disagrees with each other at the 1&sgr; level. We propose new cosmological models for the Big‐Bang nucleosynthesis to try to recover the concordance of &OHgr;B. Nuclear processes in the Big‐Bang nucleosynthesis are similar to those in the r‐process nucleosynthesis in supernovae. Even in the nucleosynthesis of heavy elements, entropy and density in the neutrino‐driven winds of Type II supernovae are so high that nuclear statistical equilibrium favors production of abundant light nuclei. In such explosive circumstances many radioactive light‐to‐intermediate mass nuclei as well as heavy mass nuclei play the significant roles. © 2004 American Institute of Physics