Spontaneous magnetization of a vacuum in the hot Universe and intergalactic magnetic fields

TL;DR

This paper reviews the spontaneous magnetization of non-Abelian gauge field vacuum at high temperatures, exploring its stability, properties, and potential role in generating intergalactic magnetic fields during the early Universe.

Contribution

It provides a detailed analysis of vacuum magnetization mechanisms, stability conditions, and estimates of magnetic field strengths relevant to cosmological magnetic phenomena.

Findings

Magnetic fields are stable and temperature-dependent in the high-temperature phase.

The magnetic mass of chromomagnetic fields is zero, similar to U(1) magnetic fields.

Estimated magnetic field strength at electroweak temperature is around 10^{14} G.

Abstract

We review the spontaneous magnetization of the vacuum of non-Abelian gauge fields at high temperature. The standard model of particles is investigated as a particular example. By using both analytic methods of quantum field theory and gauge field theory on a lattice, we determine the Abelian (chromo)magnetic fields in the restored phase of the model at high temperatures $T \geq T_{ew}$. The fields are stable and temperature dependent, $B = B(T)$. We investigate the mechanisms of the field stabilization in detail. The screening parameters for electric and magnetic fields - the Debye, $m_D(B,T),$ and magnetic, $m_{magn.}(B,T)$, masses - are calculated. It is shown that, in the field presence, the former one is smaller than at zero field. The magnetic mass of the (chromo)magnetic fields is determined to be zero, as for usual $U(1)$ magnetic field. We also show that the vacuum magnetization stops at temperatures below the electroweak phase transition temperature, $T \leq T_{ew}$, when a scalar condensate creates. These properties make reasonable a possibility that the intergalactic magnetic fields observed recently were spontaneously generated in the hot Universe at the reheating epoch due to vacuum polarization of non-Abelian gauge fields. We present a procedure for estimating the field strengths $B(T)$ at different temperatures. In particular, the value of $B(T_{ew}) \sim 10^{14} G$, at $T_{ew}$ is estimated with taking into consideration the observed intergalactic magnetic field $B_0 \sim 10^{- 15} G$. The magnetic field scale is also estimated. Some model dependent peculiarities of the phenomena studied are briefly discussed.