Spectrum of QCD nucleation-site separations and primordial nucleosynthesis

The spectrum of nucleation-site separations in the cosmic QCD phase transition is calculated within the framework of homogeneous nucleation theory. This spectrum has the property that the ratio of the standard deviation of the separations to the mean separation has the constant value of 0.466, independent of any QCD physics parameters. When the assumption is made that a duality exists between nucleation sites and baryon fluctuation sites, the same spectrum may be applied to baryon-number fluctuation separations. When nucleosynthesis results are averaged over this spectrum, the upper limit on Ωb(2.735K/T0)3x(H0/50 km s-1Mpc-1)2, as derived from the observed upper limit to the primordial 4He abundance, drops from 0.8 to 0.56 in baryon inhomogeneous universes. In order for macroscopic baryon inhomogeneities to arise in the early Universe, persist to the era of nucleosynthesis, and give nucleosynthesis yields which allow Ωb to be greater than the limit from standard big-bang nucleosynthesis, the QCD surface tension must be near its upper limit of around the cube of the coexistence temperature