Topological structures, gravitational waves and dark matter in Grand Unified Theories

Abstract

In this thesis we explore the interplay between topological structures, gravitational waves, and dark matter in Grand Unified Theories, focusing on SO(10) and E_6. We uncover composite topological structures from the spontaneous breaking of SO(10) to the Standard Model, including string networks forming necklaces, dumbbells connecting monopoles with antimonopoles, and walls bounded by necklaces. By examining these structures before and after electroweak symmetry breaking, we discuss their early-universe formation and gravitational wave implications. Extending to E_6, we consider topological structures emerging from its breaking via SO(10), including novel scenarios for producing metastable and current-carrying strings. We analyze the stochastic gravitational wave background from these strings, finding compatibility with observations, including recent NANOGrav data. We investigate third-family quasi-Yukawa unification within a supersymmetric framework, finding viable sparticle mass spectra and stable dark matter candidates. We highlight collider-accessible gluino solutions, and heavy Higgsino-like states compatible with dark matter relic density and direct detection experiments. Collectively, these studies provide insights into the formation and evolution of topological structures in Grand Unified Theories, their gravitational wave signatures, and their roles in dark matter phenomenology, offering novel perspectives on the early universe's evolution and guiding future experimental searches.