Eur. Phys. J. C (2012) 72: 1968
https://doi.org/10.1140/epjc/s10052-012-1968-3

Regular Article - Theoretical Physics

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

¹ Institute for Space Science, ICE-CSIC and IEEC, Campus UAB, Bellaterra, 08193, Barcelona, Spain
² Dnipropetrovsk National University, 49010, Dnipropetrovsk, Ukraine

^* e-mail: elizalde@ieec.uab.es
^** e-mail: elizalde@math.mit.edu

Received: 14 February 2012
Revised: 12 March 2012
Published online: 5 April 2012

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)∼10¹⁴ G at the electroweak phase transition temperature is derived by taking into consideration the present value of the intergalactic magnetic field strength, B ₀∼10⁻¹⁵ G, coherent on the ∼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.