Nucleosynthesis in the Early Universe and the test of Big Bang Model

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Standard big bang cosmology gives us a simple and natural picture of our universe since it explains the origin of cosmic microwave background and abundances of light elements, ^4He, D,^3He and ^7Li. The standard big bang nucleosynthesis (SBBN) has a single free parameter, i.e. baryon to photon number ratio eta=n_B/n_<gamma> where n_B and n_<gamma> are the number densities of baryons and photons. Comparing SBBN predictions with abundances of light elements inferred from observational data, we obtain the baryon density of the universe, OMEGA_b<approximately equal>0.01.Recently, however, it is reported that there is the discrepancy between big bang nucleosynthesis theory and observations (BBN crisis). We show that BBN predictions agree with the primordial abundances of light elements, ^4He, D,^3He and ^7Li inferred from the observational data if an electron neutrino has a net chemical potential xi_<nue> due to lepton asymmetry. We estimated that xi_<nue>=0.043^<+0.040>_<040> (95% C.L.) and OMEGA_bh^2=0.015^<+0.006>_<003> (95% C.L.). We also investigated in detail nucleosynthesis in inhomogeneous universe model, and confirmed that essentially the constraint on the baryon to photon number ratio from light element observations is the same as that of standard model, since the observation of Li gives stringent limit to the density contrast of the inhomogeneity.