Baryon inhomogeneity generation via cosmic strings at QCD scale and its effects on nucleosynthesis

We have earlier shown that cosmic strings moving through the plasma at the time of a first order quark-hadron transition in the early universe can generate large scale baryon inhomogeneities. In this paper, we calculate detailed structure of these inhomogeneities at the quark-hadron transition. Our calculations show that the inhomogeneities generated by cosmic string wakes can strongly affect nucleosynthesis calculations. A comparison with observational data suggests that such baryon inhomogeneities should not have existed at the nucleosynthesis epoch. If this disagreement holds with more accurate observations, then it will lead to the conclusions that cosmic string formation scales above $10^{14} - 10^{15}$ GeV may not be consistent with nucleosynthesis and CMBR observations. Alternatively, some other input in our calculation should be constrained, for example, if the average string velocity remains sufficiently small so that significant density perturbations are never produced at the QCD scale, or if strings move ultra-relativistically so that string wakes are very thin, trapping negligible amount of baryons. Finally, if quark-hadron transition is not of first order then our calculations do not apply.