Topological defects in cosmology and nuclear physics

• Main Author: Damodaran, K.
• Published: University of Cambridge 2000
• Subjects: 520
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.598261

This dissertation is concerned with topological defects that arise from symmetry breaking in the non-linear sigma model limits of scalar field theories. The nonlinear evolution of global topological defects in <I>O</I> (<I>N</I>) field theories provide a mechansims for sourcing hte cosmic microwave background (CMB) temperature anisotropy on the sky today. In these theories, <I>N </I>determines the type of defect based on the homotopy group of the underlying vacuum manifold. Additionally, in models of nuclear physics based on <I>SU </I>(2) gauge theories, π<SUB>3</SUB> defects can manifest themselves as static soliton solutions. A simple class of <I>O</I> (<I>N</I>) scalar fields are studied here. The defects considered were strings with <I>N</I> =2, monopoles with <I>N</I> =3, textures with <I>N</I> = 4 and a class of "non-topological" textures, with <I>N</I> =6. Calculations of the temperature anisotropy are computationally challenging. High precision is needed in order to cmopare predictions with new and future CMB observations. The anisotropy is calculated from the classic Sachs-Wolfe formula by using a real space evolution for the matter and radiatino fluids. In order to properly account for diffusion damping and the finnite thickness of the last scattering surface, the power spectra were compared to high precision calculations based on defect source stress energy tensor unequal-time correlators. Matching the tails of the spectra yielded an angualr smoothing scale <I>l <SUB>D</SUB> </I>for the fluctuation maps. Ensembles of 10° maps of the sky today were produced for each defect. Defects also have implications in modesl of nucelar physics. The first π<SUB>3</SUB> soliton to be studied in nuclear physics was the Skyrmion, a topological solution to the nonlinear sigma model for pion fields. Skyrme introduced a four-derivative term to stabilize the soliton. Alternatively one could introduce gauge fields to stabilize the texture. It is shown that the presence of an extra identical Higgs doublet in a gauged <I>SU </I>(2) nonlinear sigma model can produce soliton solutions. The solution is related to the Sphaleron and Electroweak Skyrmion in the Standard Model, but unlike these solitons, it is dyanmically stable to small spherically symmetric perturbations. A similar solution is shown to exist in the Vector Dominance model, with <I>p</I>-mesons representing the gauge bosons of a hidden local <I>SU</I> (2) gauge symmetry of the nonlinear sigma model. This is in agreement with similar work done by Igarashi, Johmuar, Kobayashi, Otsu, Sato and Sawada.