Cosmological phase transitions: extra dimensions and black holes

Early Universe cosmological phase transitions, in particular first-order transitions which proceed through the nucleation of bubbles, provide an environment for interesting physics with potentially detectable consequences. This thesis focuses broadly on bubble nucleation rates and the determination of a successful transition. After providing the groundwork for understanding these transitions and their key characteristics, this work can be considered in two main parts: improving viability of the extra-dimensional holographic phase transition, and quantifying the effect of black holes acting as nucleation sites for thermal phase transitions. Extra dimensional models recently gained traction as attractive options for solving the hierarchy problem, one of physics’ most prominent issues. Finite temperature studies of the Randall-Sundrum model, one of the most popular models, revealed the existence of the holographic phase transition, a first-order transition described by the radion field. Typically, however, this transition struggles to complete while maintaining a consistent theory. Applying knowledge from more conventional settings, this thesis firstly describes work to alleviate this problem through the introduction of brane localised curvature, altering the kinetic term of the radion field. Ultimately, it is shown that nucleation rates sufficient for a successful phase transition can be achieved over a large region of parameter space. Nevertheless, difficulties remain when describing the role of black holes in holographic phase transitions. Inspired by these issues, the second key work of this thesis studies the possibility of black holes acting as nucleation sites in thermal phase transitions. Within the thin-wall limit, it is found that lower mass black holes could drastically improve nucleation rates. Consequently, future studies of cosmological phase transitions should carefully consider the effect of black holes; particularly in regards to phenomenological outcomes such as gravitational waves.