The Electrical Conductivity in the Early Universe

Abstract

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, $\ddot{I}{ƒ}_{el}\sim T/\hat{I}\pm \ln (1/\hat{I}\pm )$, 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 $\ddot{I}{ƒ}_{el}/T$ being only a factor $\sim {\cos }^4\hat{I}{¸}_W$ smaller than at temperatures below $T_c$.

11 pages including 2 figures