Spontaneous magnetization of the vacuum and the strength of the magnetic field in the hot Universe

TL;DR

This paper explores the spontaneous generation of magnetic fields in the early Universe due to vacuum polarization effects, estimating their strength at different temperatures and implications for intergalactic magnetic fields.

Contribution

It develops a method to estimate magnetic field strengths during the early Universe, considering vacuum polarization and zero screening mass, with specific estimates at the electroweak transition.

Findings

Estimated magnetic field strength at electroweak transition: ~10^{14} G

Linked early Universe magnetic fields to present intergalactic fields (~10^{-15} G)

Discussed model-dependent properties of vacuum polarization phenomena

Abstract

Intergalactic magnetic fields are assumed to have been spontaneously generated at the reheating stage of the early Universe, due to vacuum polarization of non-Abelian gauge fields at high temperature. The fact that the screening mass of this type of fields has zero value was discovered recently. A procedure to estimate their field strengths, $B(T)$, at different temperatures is here developed, and the value $B(T_{ew}) \sim 10^{14} G$ at the electroweak phase transition temperature, is derived by taking into consideration the present value of the intergalactic magnetic field strength, $B_0 \sim 10^{- 15} G$, coherent on the $\sim 1$ Mpc scale. As a particular case, the standard model is considered and the field scale at high temperature is estimated in this case. Model dependent properties of the phenomena under investigation are briefly discussed, too.