We review the recent progress in the Big-Bang nucleosynthesis which includes the standard and non-standard theory of cosmology, effects of neutrino degeneracy, and inhomogeneous nucleosynthesis within the framework of a Friedmann model. As for a non-standard theory of gravitation, we adopt a Brans-Dicke theory which incorporate a cosmological constant. We constrain various parameters associated with each subject

Comparing the latest observed abundances of 4 He and D, we make a χ 2 analysis to see whether it is possible to reconcile primordial nucleosynthesis using up-to-date nuclear data of NACRE II and the mean-life of neutrons. If we adopt the observational data of 4 He by Izotov et al.[1], we find that it is impossible to get reasonable concordance against the standard Big-Bang nucleosynthesis.However, including degenerate neutrinos, we have succeeded in obtaining consistent constraints between the neutrino degeneracy and the baryon-to-photon ratio from detailed comparison of calculated abundances with the observational data of 4 He and D: the baryon-to-photon ratio in units of 10 −10 is found to be in the range 6.02 η 10 6.54 for the specified parameters of neutrino degeneracy.

One of the main purpose in cosmology is to determine an equation of the state (EoS) of dark energy (DE). DE dominates the evolution of our universe. Since DE is currently in dominant phase, it accelerates our universe. Usually the feature of DE is classified as canonical or non-canonical field by the value of EoS if it is more than -1. To understand the behavior of DE, type Ia supernovae (SNe Ia) are often used. In addition to this, gamma-ray bursts (GRBs) are also studied to disclose its properties because it can be found at high redshift region. These studies indcates that GRBs can be the candidate of the cosmological proves. For instance, Yonetoku relation and Amati relation are established. These relation can be used to constrain the cosmological models. In this work, we apply an EoS which varies over time and reveal the density evolution of DE. Then, we use Markov chain Monte Calro method to constrain the EoS from the SNe Ia and GRBs. We find that DE prefers that there is a crossing of the phantom barrier near our time.