Phase transition magnetic fields

During the history of the Universe several cosmological phase transitions have taken place. The best studied are: QCD (250 MeV), electroweak (10² GeV) and GUT (10¹⁶GeV). For a comparison, consider that the present epoch is characterized by 3 × 10^-4 eV, the matter-radiation decoupling by 1 eV and the nucleosynthesis epoch by 1 MeV. Typical values of the horizon scale correspond to a present-day 0.2 pc for the QCD transition, 3 × 10¹⁴ cm for the electroweak transition and 1 m for GUT.

Hogan (1983) proposed first order phase transitions as a potential magnetogenetic mechanism. Phase transitions would not have taken place simultaneously throughout the Universe, but in causal bubbles. At the rim of these bubbles high gradients of temperature or any other parameter characterizing the phase transition (for instance, the Higgs vacuum expectation value) would be established. These high gradients could produce a thermoelectric mechanism akin to the Biermann battery. Magnetic reconnection would stitch the magnetic field lines of different bubbles and the magnetic field lines would execute a Brownian walk.

There exist a large variety of works and ideas. The electroweak transition has been considered as a source of magnetic fields by Vachaspati (1989), Enqvist and Olesen (1993), Davidson (1996), Grasso and Rubinstein (1995) and others. The QCD phase transition as a magnetogenesis mechanism has been studied by Quashnock, Loeb and Spergel (1989), Cheng and Olinto (1994) and others. Magnetic fields generated at the GUT phase transition have been analyzed by Davies and Dimopoulos (1995), Brandenberger et al. (1992). Other interesting theories related to Cosmological phase transitions have been proposed by Vachaspati and Vilenkin (1991), Kibble and Vilenkin (1995), Baym, Boedeker and McLerran (1996) and others.

From the equations for magnetic fields produced at a given phase transition, and the spectra at different length scales given by Vachaspati (1989) it is deduced (Battaner and Lesch, 2000) that B, the equivalent-to-present magnetic strength, only depends on T₀² (where T₀ is the present CMB temperature) and that the spectrum B₀($\lambda$) only depends on T₀/$\lambda$ (or on T₀^3/2$\lambda^{-1/2}_{}$ with a correction proposed by Enquist and Olesen (1993)). In any case the present spectrum of magnetic strength for different scales B₀($\lambda$) is independent of the specific phase transition. There is one compensation: earlier phase transitions produced larger magnetic fields but they have had longer to be weakened by expansion. We will comment later that the values of B₀ can differ greatly from present magnetic field strengths.