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

11 pages including 2 figures