Leptogenesis in the symmetric phase of the early universe: Baryon asymmetry and hypermagnetic helicity evolution
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, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Leptogenesis in the Symmetric Phase of the Early Universe: Baryon Asymmetry and Hypermagnetic Helicity Evolution V. B. Semikoza,* and A. Yu. Smirnova,b a
Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Russian Academy of Sciences (IZMIRAN), Troitsk, Moscow oblast, 142190 Russia bNational University of Science and Technology “MISIS,” Moscow, 119991 Russia *email: [email protected] Received July 15, 2014
Abstract—We investigate the evolution of the baryon asymmetry of the Universe (BAU) in its symmetric phase before the electroweak phase transition (EWPT) induced by leptogenesis in the hypermagnetic field of an arbitrary structure and with a maximum hypermagnetic helicity density. The novelty of this work is that the BAU has been calculated for a continuous hypermagnetic helicity spectrum. The observed BAU Bobs = 10 ⎯10 that can be in largescale hypermagnetic fields satisfying the wave number inequality k ≤ kmax grows with increasing kmax. We will also show that the initial righthanded electron asymmetry ξeR(η0) used in our leptogenesis model as a free parameter cannot take too large values, ξeR(η0) = 10–4, because this leads to a negative BAU by the EWPT time. In contrast, a sufficiently small initial righthanded electron asymmetry, ξeR(η0), provides its further growth and the corresponding BAU growth from zero to some positive value, including the observed Bobs = 10–10. DOI: 10.1134/S1063776115020053
1. INTRODUCTION Astrophysical magnetic fields affect the cosmicray propagation, the stellar (solar) activity, etc., while their origin is still an open question in astrophysics and cosmology [1–3]. Since Maxwell’s equations are lin ear in fields E and B, there must be some seed (mag netic) field needed to switch on a dynamo leading to field amplification to the observed galactic magnetic field strengths, Bgal ~ 10–6 G. There are two possibili ties of searching for such a seed in a galaxy: (i) an astrophysical one, for example, in scenarios that take into account supernova explosions with the ejection of a magnetohydrodynamic (MHD) plasma with a fro zenin magnetic field into intergalactic space and (ii) a cosmological scenario that envisages the exist ence of seed fields (and considers their evolution) over the radiationdominated and dustlike stages of the early Universe. In this paper, we rely on the second scenario (ii). An upper limit on the cosmological mag netic field (CMF), B < 10–10–10–9 G, has long been known, for example, from observations of the Faraday rotation of the radioemission polarization plane [4]. The first evidence for the presence of CMF in the intergalactic medium that can survive up to the present epoch is related to the prediction of a lower limit for the CMF amplitudes, BCMF > 10–16–10–14 G, that follows from satellite observations of highenergy photons (in particular, from the Fermi experiment) [5, 6], which is a new confirmation of the CMF concept used here.
In this paper, we will be inter
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