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, $T_c\simeq 100\mathrm{GeV}.$ Debye and dynamical screening of electric and magnetic interactions leads to a finite conductivity, ${\sigma }_{\mathrm{el}}\sim T/\alpha \ln (1/\alpha ),$ 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 ${\sigma }_{\mathrm{el}}/T$ being only a factor $\sim {\cos }^4{\theta }_W$ smaller than at temperatures below $T_c.$