Production of free quarks in the early universe

A model of the $q-\overline{q}$ interaction which avoids complete confinement is employed to calculate the number of free quarks which survive from the early universe. For a free-quark mass $M\lesssim 10$ GeV, our results are similar to those of previous calculations. But for $M\gtrsim 10$ GeV, the number per nucleon is given by $\ln \left(\frac{q}{N}\right)=\ln \left(\frac{\overline{q}}{N}\right)=-\frac{M}{k{T}_{*}}+2\mathrm{}\ln \left(\frac{M}{k{T}_{*}}\right)+C$, where the constant $C\simeq 20$. Quarks of such mass freeze out of equilibrium during the quark-hadron transition at a temperature $0.2\lesssim T_{*}\lesssim 0.4$ GeV/k, which for instance predicts $15\lesssim M\lesssim 30$ GeV if $\frac{(q+\overline{q})}{N}\sim {10}^{-20\mathrm{}}$.