The Electrical Conductivity in the Early Universe

We calculate the electrical conductivity in the early universe at temperatures below as well as above the electroweak vacuum scale, $T_c\simeq 100$GeV. Debye and dynamical screening of electric and magnetic interactions leads to a finite conductivity, ${\sigma }_{el}\sim T\mathrm{/}\alpha \ln (1\mathrm{/}\alpha )$, at temperatures well below $T_c$. At temperatures above, $W^{\pm }$ charge-exchange processes – analogous to color exchange through gluons in QCD – effectively stop left-handed charged leptons. However, right-handed leptons can carry current, resulting in ${\sigma }_{el}\mathrm{/}T$ being only a factor $\sim {\cos }^4{\theta }_W$ smaller than at temperatures below $T_c$.