Supercooled cosmological phase transitions: impacts on phase histories and gravitational wave predictions

The events of the very early Universe are still largely a mystery. Cosmological phase transitions are important events that change how particles behave universally, and identifying them can lead to revolutionary insights into new physics. Some phase transitions release vast quantities of energy and lead to gravitational waves possibly observable today. Predicting the corresponding gravitational wave signal requires a series of very challenging calculations. This thesis explores these calculations and the uncertainties and ambiguities involved, and provides the details necessary for careful treatment of gravitational wave predictions.