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, $\sigma_{el}\sim T/\alpha\ln(1/\alpha)$, 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 $\sigma_{el}/T$ being only a factor $\sim \cos^4\theta_W$ smaller than at temperatures below $T_c$.