Symmetry Breaking: Magnetic Fields in Cosmology

This lecture discusses the phenomenon of symmetry breaking, particularly focusing on electroweak symmetry breaking and its implications for magnetic fields in the universe. The instructor begins by explaining spontaneous symmetry breaking and the formation of topological defects, such as cosmic strings, which arise from a complex scalar field. The discussion progresses to the electroweak symmetry breaking, where a complex doublet of fields leads to a vacuum manifold represented as a three-dimensional sphere. The Kibble mechanism is introduced, highlighting how different domains can choose different angles, leading to the emergence of magnetic monopoles connected by strings. The instructor elaborates on the definition of electromagnetic fields and the gauge invariance required for their formulation. The evolution of magnetic fields during electroweak symmetry breaking is examined, with simulations showing that a significant portion of vacuum energy converts into magnetic fields. The lecture concludes with insights into the present-day magnetic field estimates and their potential connections to CP violation in particle physics, emphasizing the importance of understanding these magnetic structures in cosmology.