Production of free quarks in the early universe

Abstract

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