Spectra of magnetic fields injected during baryogenesis

Abstract

Helical magnetic fields are injected into the cosmic medium during cosmological baryogenesis and can potentially provide a useful probe of the early universe. We construct a model to study the injection process during a first order phase transition and to determine the power spectra of the injected magnetic field. By Monte Carlo simulations we evaluate the Fourier space symmetric and helical power spectra of the magnetic field at the time the phase transition completes. The spectra are peaked at the scale given by the inverse size of bubbles at percolation and with a comparable width. These injected magnetic fields set the initial conditions for further cosmological magnetohydrodynamical evolution.Our study of the universe relies on relics left-over from early cosmological epochs. The cosmic microwave background brings information from the epoch when atoms formed, the light elemental abundances from the epoch when nuclei formed. Similarly, the electroweak phase transition may mark the epoch when a net baryon number was generated, or when net lepton number was converted into net baryon number, and this coincides with the generation of magnetic fields. The present paper is based on the hypothesis that primordial magnetic fields will inform us of the epoch when a net amount of baryons first formed, the so-called epoch of "baryogenesis" [1,2].The question of whether a primordial magnetic field exists is often raised in connection with the magnetic fields observed in galaxies and clusters of galaxies with strength ∼ µG and kpc-Mpc coherence scale. There is considerable debate whether primordial fields are essential to the generation of galactic fields, and what properties of the primordial field are necessary to turn them into observed magnetic structures. The arguments involve the coherence and amplitude of observed magnetic fields, the efficiency of galactic dynamos, the turnover time scales associated with galactic dynamics, especially with the earliest known galaxies containing magnetic structures, astrophysical sources e.g. active galactic nuclei that may spew out magnetic fields, and the generation of large scale seed fields by the Biermann battery. We shall by-pass these issues since, in our view, a primordial magnetic field is of interest in itself, whether or not it is responsible for the observed magnetic fields in galaxies. If there are strongly motivated early universe scenarios, based on reasonably well-established particle physics, that lead to the generation of magnetic fields, they provide good reason to study and to look for these structures in cosmological data.The connection between baryon number production and primordial magnetic fields can be understood intuitively in the following way. Baryon number violation in the standard model of the electroweak interactions is made possible due to a quantum anomaly. As a physical process, baryon number is generated when many different particles come together to form an object called a "sphaleron" [3,4], which then decays into a final state with baryon number...

Progress on Cosmological Magnetic Fields

“…Several groups have applied numerical techniques to study the electroweak phase transition and the properties of the magnetic fields that are generated [132][133][134][135][136][137]. So far the simulations have only considered the bosonic sector of the electroweak model.…”

Primordial magnetism in the CMB: Exact treatment of Faraday rotation and WMAP7 bounds

“…Of particular interest to us are magnetogenesis scenarios based on phase transitions such as the electroweak phase transition, when Maxwellian electromagnetism first emerged [4][5][6][7][8][9][10][11]. In this scenario particle physics uncertainties are minimal and magnetogenesis is tightly related to the creation of matter, or "baryogenesis" -the magnitude of the magnetic helicity density is approximately equal to the baryon number density.…”

Kibble mechanism for electroweak magnetic monopoles and magnetic fields

“…An alternative approach to deriving the properties of the magnetic field is to directly simulate the electroweak symmetry breaking, as has been done in several works [29][30][31][32][33]. These field theory simulations are much more computationally intensive than the present approach and are limited by computer resources.…”