Diffusion coefficients and constraints on hadronic inhomogeneities in the early universe

Hadronic inhomogeneities are formed after the quark hadron phase transition. The nature of the phase transition dictates the nature of the inhomogeneities formed. Recently some scenarios of inhomogeneities have been discussed where the strange quarks are in excess over the up and down quarks. The hadronization of these quarks will give rise to a large density of hyperons and kaons in addition to the protons and neutrons which are formed after the phase transition. These unstable hyperons decay into pions, muons and their respective neutrinos. Hence the plasma during this period consists of neutrons, protons, electrons, muons and neutrinos. Due to the decay of the hyperons, the muon component of the inhomogeneities will be very high. We study the diffusion of neutrons and protons in the presence of a large number of muons immediately after the quark hadron phase transition. We find that the presence of the muons enhances the diffusion coefficient of the neutrons/protons. As the diffusion coefficient is enhanced, the inhomogeneities will decay faster in the regions where the muon density is higher. Hence smaller muon rich inhomogeneities will be completely wiped out. The decay of the hyperons will also generate muon neutrinos. Since the big bang nucleosynthesis provides constraints on the neutrino degeneracies, we revisit the effect of non zero degeneracies on the primordial elements.