Broken Symmetries at High Temperature as a Solution to the Domain Wall and Monopole Problems

More than 30 years after it was suggested that topological defects may be produced in a cosmological phase transition, the monopole and the domain wall problems remain some of the most interesting open issues in the field of astroparticle physics. This is particularly true for the monopole problem, a consequence of an idea. as fundamental as grand unification in particle physics. Although several solution have been suggested, among them the far-reaching proposal of an inflationary period during the evolution of the rniverse, the problems are still far from solved. On the contrary, in the domain wall case it is frequently proposed to altogether abandon the possibility of spontaneous breakdown of discrete symmetries in general. The idea of this Thesis is to investigate how fundamental the incompatibility of the standard cosmological model is with theories that admit domain wall or monopole solutions. Topological defect production in cosmological phase transitions has been my main interest during these years at SISSA. Having studied the formation of strings in first-order phase transitions in collaboration first with Leandros Perivolaropoulos. and later with Antonio Ferrera, it was natural to turn to the more "dangerous:· defects -domain walls and monopoles. Research in this direction was carried out mainly with Goran Senjanovic, and in collaboration with Gia Dvali and Barut Bajc. It is this later work which will be presented in this Thesis. The first chapter concerns the generalities of topological defect production in a cosmological context. After a brief review of phase transitions in theories with spontaneous symmetry breaking, topological defects are introduced, and the mechanism of its production is described. Some specific calculations in thermal field theory are left for the Appendix. The second chapter is the central one, where the monopole and domain wall problems are described, together with a review of the solutions proposed in the literature. It is in this chapter that the proposal of this Thesis is presented; namely, that phase transitions are not unavoidable in theories of symmetry breaking with more than one scalar field. A general discussion is offered on how this can eliminate the domain wall and monopole problem. In the last three chapters the original results are presented. Chapter 3 is devoted to discrete symmetries and domain walls, Chapter 4 to gauge symmetries and monopoles. In Chapter .5 the high-temperature behavior of non-renormalizable theories is studied, with results on supersymmetric theories.