We investigate the observational constraints on the inhomogeneous big-bang nucleosynthesis that Matsuura et al. (2005) suggested that states the possibility of the heavy element production beyond 7Li in the early universe. From the observational constraints on light elements of 4He and D, possible regions are found on the plane of the volume fraction of the high-density region against the ratio between high- and low-density regions. In these allowed regions, we have confirmed that the heavy elements beyond Ni can be produced appreciably, where p- and/or r-process elements are produced well simultaneously. 1. Introduction Big-bang nucleosynthesis (BBN) has been investigated to explain the origin of the light elements, such as , D, , and , during the first few minutes [1–4]. Standard model of BBN (SBBN) can succeed in explaining the observation of those elements, [5–9], D [10–13], and [14, 15], except for . The study of SBBN has been done under the assumption of the homogeneous universe, where the model has only one parameter, the baryon-to-photon ratio . If the present value of is determined, SBBN can be calculated from the thermodynamical history with the use of the nuclear reaction network. We can obtain the reasonable value of by comparing the calculated abundances with observations. In the meanwhile, the value of is obtained as [1] from the observations of and D. These values agree well with the observation of the cosmic microwave background: [16]. On the other hand, BBN with the inhomogeneous baryon distribution also has been investigated. The model is called as inhomogeneous BBN (IBBN). IBBN relies on the inhomogeneity of baryon concentrations that could be induced by baryogenesis (e.g., [17]) or phase transitions such as QCD or electro-weak phase transition [18–21] during the expansion of the universe. Although a large-scale inhomogeneity is inhibited by many observations [16, 22–24], a small scale one has been advocated within the present accuracy of the observations. Therefore, it remains a possibility for IBBN to occur in some degree during the early era. In IBBN, the heavy element nucleosynthesis beyond the mass number has been proposed [17, 18, 25–35]. In addition, peculiar observations of abundances for heavy elements and/or could be understood in the way of IBBN. For example, the quasar metallicity of C, N, and Si could have been explained from IBBN [36]. Furthermore, from recent observations of globular clusters, a possibility of inhomogeneous helium distribution is pointed out [37], where some separate groups of different main sequences
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