Cosmic necklaces in string theory and field theory

Abstract

In this thesis we investigate astrophysical phenomena which arise in models with compact extra dimensions, focussing on the cosmological consequences of strings which wrap cycles in the internal space. Embedding our strings in the Klebanov-Strassler geometry we develop a concrete model of cosmic necklaces and investigate the formation of primordial black holes and dark matter relics from necklace collapse. Using data from the EGRET cosmic ray experiment, we place bounds on the parameters which de ne the warped deformed conifold, including the value of the warp factor and the radius of the compact space. Chapter 1 provides a brief overview, while background material is included in chapter 2, and these results are presented in chapter 3. In chapter 4 we analyse the dynamics of wound strings with angular momentum in the compact dimensions and determine the equation of motion for a self-oscillating loop. Finally, in chapter 5 we suggest a eld-theoretic dual for wound-string necklaces based on a modi cation of the standard Abelian-Higgs model. After introducing spatially-dependent couplings for the scalar and vector elds, we propose a static, non-cylindrically symmetric solution of the resulting eld equations which describes a \pinched" string with neighbouring vortex and anti-vortex regions. The similarities between pinched strings and the four-dimensional appearance of wound-string states are then examined and a correspondence between eld theory and string theory parameters is suggested. We nd that the topological winding number of the eld theory vortex may be expressed in terms of parameters which de ne the winding of the dual string around the compact space. According to this relation, the topological charge is equal to unity when the string has zero windings, and the standard Nielsen-Olesen duality is recovered in this limit. One key result of this work is an estimate of the Higgs boson mass (at critical coupling) in terms of the parameters which de ne the Klebanov-Strassler geometry and which, in principle, may be constrained by cosmological observations.