First order phase transitions beyond the Standard Model

Gravitational waves have had a long and interesting history, and recently have been experimentally confirmed. This and the fact that many areas of physics are beyond the reach of traditional observational prospects has been the catalyst to new space-based gravitational wave detectors such as LISA being proposed and confirmed for the near future. Cosmological phase transitions in the early Universe proceed through bubble nucleation and collision if they are first-order which is thought to produce gravitational waves which could be detected by these missions, and so a great effort is being expended to scrutinise how these transitions would proceed and what their controlling factors are. Aspects of these transitions are difficult to determine however due to most knowledge being limited to the perturbative regime where couplings are weak, a limitation which is not necessarily fulfilled by these scenarios. In this thesis I study the nature of these phase transitions and the type of gravitational waves they could produce, and then take advantage of the nature of the AdS/CFT correspondence (also called the gauge/gravity duality or holographic principle) which translates strongly-coupled field theories to weakly-coupled higher dimensional gravitational theories to be able to reframe the difficult problems in these transitions into more easily tractable versions. Using this approach I find techniques to determine the most important parameters that control the phase transition, generally scanning across a broad range of parameter spaces to ascertain generic features, and then use these to establish whether detectable gravitational wave signals will be produced in the models I consider.