Electrical Conduction in the Early Universe

TL;DR

This paper calculates the electrical conductivity of the early universe across different temperature regimes, revealing how screening effects and particle interactions influence conductivity near the electroweak scale.

Contribution

It provides a detailed calculation of electrical conductivity in the early universe, accounting for screening effects and charge exchange processes at temperatures below and above the electroweak scale.

Findings

Conductivity is finite due to screening effects at all temperatures.

Above the electroweak scale, charge exchange processes suppress left-handed lepton conductivity.

Right-handed leptons maintain significant conductivity above the electroweak scale.

Abstract

The electrical conductivity has been calculated 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 $T_c$.