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Symmetry, Integrability and Geometry: Methods and Applications SIGMA 6 (2010), 053, 10 pages Cosmological Symmetry Breaking and Generation of Electromagnetic Field? Michiyasu NAGASAWA Department of Information Science, Kanagawa University, Tshuchiya 2946, Hiratsuka-shi, Kanagawa-ken, 259-1293 Japan E-mail: [email protected] Received November 15, 2009, in final form May 14, 2010; Published online June 29, 2010 doi:10.3842/SIGMA.2010.053 Abstract. Cosmological phase transitions accompanied by some kind of symmetry breaking would cause the creation of topological defects and the resulting production of primordial magnetic field. Moreover, such a procedure inevitably affects the cosmic background ra- diation and it may be observed today. Motivated by the existence of stabilized embedded defects in the standard model of elementary interactions, we discuss their application to the cosmological electromagnetic field generation. Key words: cosmology; defect; pion string; magnetic field 2010 Mathematics Subject Classification: 83F05 1 Introduction Particle cosmology predicts that our universe has experienced some phase transitions associated with the unification theory of the interactions. One of the important applications of such a transition to the cosmic evolution would be the generation of topological defects [1]. These defects are topologically stable and whether their formation is possible or not and the type of their structure can be judged by the way of symmetry breaking at the phase transition. In addition to conventional topologically stable defects, another kind of cosmological defects are suggested as an interesting product in the early universe [2]. Even when the topologically charged configuration is not to be prevented from becoming a trivial one, such a field configuration can be constructed so that it satisfies the equation of motion although it is not energetically preferable. That is, embedded defects are unstable at zero temperature. In the early universe, however, the finite temperature plasma existed so that they can be stabilized because of the asymmetry between charged and neutral scalar components [3]. At the low temperature, the photon decoupling occurs on the other hand. Then defects undergo core phase transition and/or decay, which might bring primordial magnetic field generation. Although at present there exist magnetic fields in various astrophysical scales, the origin of galactic magnetic fields ∼ 10−6 G is not revealed completely [4]. We will see pion strings can provide seed magnetic fields which evolve to present large scale fields. Note that, in addition, some kinds of effects on cosmic microwave background radiation could be observed by the interaction between pion fields and cosmic background photons. A cosmic string is a two-dimensional defect and it is widely investigated since it has various cosmological significances. If the effective potential has the form of a Mexican hat, a phase tran- sition accompanied by some kind of symmetry breaking occurs and cosmic strings are produced. ?This paper is a contribution to the Proceedings of the Eighth International Conference “Symmetry in Nonlinear Mathematical Physics” (June 21–27, 2009, Kyiv, Ukraine). The full collection is available at http://www.emis.de/journals/SIGMA/symmetry2009.html

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