Abstract:
We consider the effect of inhomogeneous neutrino degeneracy on Big Bang nucleosynthesis for the case where the distribution of neutrino chemical potentials is given by a Gaussian. The chemical potential fluctuations are taken to be isocurvature, so that only inhomogeneities in the electron chemical potential are relevant. Then the final element abundances are a function only of the baryon-photon ratio $\eta$, the effective number of additional neutrinos $\Delta N_\nu$, the mean electron neutrino degeneracy parameter $\bar \xi$, and the rms fluctuation of the degeneracy parameter, $\sigma_\xi$. We find that for fixed $\eta$, $\Delta N_\nu$, and $\bar \xi$, the abundances of helium-4, deuterium, and lithium-7 are, in general, increasing functions of $\sigma_\xi$. Hence, the effect of adding a Gaussian distribution for the electron neutrino degeneracy parameter is to decrease the allowed range for $\eta$. We show that this result can be generalized to a wide variety of distributions for $\xi$.

Abstract:
We examine Big Bang nucleosynthesis (BBN) in the case of inhomogenous neutrino degeneracy, in the limit where the fluctuations are sufficiently small on large length scales that the present-day element abundances are homogeneous. We consider two representive cases: degeneracy of the electron neutrino alone, and equal chemical potentials for all three neutrinos. We use a linear programming method to constrain an arbitrary distribution of the chemical potentials. For the current set of (highly-restrictive) limits on the primordial element abundances, homogeneous neutrino degeneracy barely changes the allowed range of the baryon-to-photon ratio. Inhomogeneous degeneracy allows for little change in the lower bound on the baryon-to-photon ratio, but the upper bound in this case can be as large as 1.1 \times 10^{-8} (only electron neutrino degeneracy) or 1.0 \times 10^{-9} (equal degeneracies for all three neutrinos). For the case of inhomogeneous neutrino degeneracy, we show that there is no BBN upper bound on the neutrino energy density, which is bounded in this case only by limits from structure formation and the cosmic microwave background.

Abstract:
We consider inhomogeneous big bang nucleosynthesis in light of the present observational situation. Different observations of He-4 and D disagree with each other, and depending on which set of observations one uses, the estimated primordial He-4 corresponds to a lower baryon density in standard big bang nucleosynthesis than what one gets from deuterium. Recent Kamiokande results rule out a favorite particle physics solution to this tension between He-4 and D. Inhomogeneous nucleosynthesis can alleviate this tension, but the more likely solution is systematics in the observations. The upper limit to Omega_b from inhomogeneous nucleosynthesis is higher than in standard nucleosynthesis, given that the distance scale of the inhomogeneity is near the optimal value, which maximizes effects of neutron diffusion. Possible sources of baryon inhomogeneity include the QCD and electroweak phase transitions. The distance scale of the inhomogeneities arising from the electroweak transition is too small for them to have a large effect on nucleosynthesis, but the effect may still be larger than some of the other small corrections recently incorporated to SBBN codes.

Abstract:
The recent Boomerang and MAXIMA data on the cosmic microwave background suggest a large value for the baryonic matter density of the universe, omega_b = 0.03. This density is larger than allowed by standard big bang nucleosynthesis theory and observations on the abundances of the light elements. We explore here the possibility of accommodating this high density in inhomogeneous big bang nucleosynthesis (IBBN). It turns out that in IBBN the observed D and Y_p values are quite consistent with this high density. However, IBBN is not able to reduce the 7Li yield by more than about a factor of two. For IBBN to be the solution, one has to accept that the 7Li plateau in population II halo stars is depleted from the primordial abundance by at least a factor of two.

Abstract:
This article describes the production of primordial He4 nuclei in an inhomogeneous universe. The baryon distribution is spherically symmetric and consists of a high density inner region and a low density outer region. As the temperature decreases neutrons diffuse to the outer region until they are homogeneously distributed, and protons may be redistributed depending on how fast diffusion occurs. Nucleosynthesis occurs earlier in the inner region and neutrons diffuse back to that region. The rapidity of diffusion determines how much He4 is ultimately produced.

Abstract:
Based on a scenario of the inhomogeneous big-bang nucleosynthesis (IBBN), we investigate the detailed nucleosynthesis that includes the production of heavy elements beyond Li-7. From the observational constraints on light elements of He4 and D for the baryon-to-photon ratio given by WMAP, possible regions 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 Fe can be produced appreciably, where p- and/or r-process elements are produced well simultaneously compared to the solar system abundances. We suggest that recent observational signals such as He4 overabundance in globular clusters and high metallicity abundances in quasars could be partly due to the results of IBBN. Possible implications are given for the formation of the first generation stars

Abstract:
The effect of the heating of neutrinos by scattering with electrons and positrons and by e-e+ annihilation on nucleosynthesis is calculated for a spherically symmetric baryon inhomogeneous model of the universe. The model has a high baryon density core and a low density outer region. The heating effect is calculated by solving the Boltzmann Transport Equation for the distribution functions of electron and muon/tau neutrinos. For a range of baryon-to-photon ratio = [ 0, 1.5 ] x 10^-10 and distance scale = [ 10^2, 10^8 ] cm the heating effect increases the mass fraction of He4 by a range of [1, 2] x 10^-4. The change of the value of the mass fraction of He4 appears similiar to the change caused by an upward shift in the value of the baryon-to-photon ratio. But the change to deuterium is a decrease in abundance ratio Y(d)/Y(p) on the order of 10^-3, one order less than the decrease due to a shift in baryon-to-photon ratio.

Abstract:
We investigate the possibility of accounting for the currently inferred primordial abundances of D, 3He, 4He, and 7Li by big bang nucleosynthesis in the presence of baryon density inhomogeneities plus the effects of late-decaying massive particles (X), and we explore the allowed range of baryonic fraction of the closure density Omega_b in such context. We find that, depending on the parameters of this composite model (characteristic size and density contrast of the inhomogeneities; mass-density, lifetime, and effective baryon number in the decay of the X-particles), values as high as \Omega_{b}h_{50}^{2}\simeq 0.25-0.35 could be compatible with the primordial abundances of the light nuclides. We include diffusion of neutrons and protons at all stages, and we consider the contribution of the X particles to the energy density, the entropy production by their decay, the possibility that the X-products could photodissociate the light nuclei produced during the previous stages of nucleosynthesis, and also the possibility that the decay products of the X-particles would include a substantial fraction of hadrons. Specific predictions for the primordial abundance of Be are made.

Abstract:
We investigate the observational constraints on the inhomogeneous big-bang nucleosynthesis that Matsuura et al. suggested the possibility of the heavy element production beyond ${}^7$Li in the early universe. From the observational constraints on light elements of ${}^4$He 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.

Abstract:
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