TASI lectures on Phase Transitions, Baryogenesis, and Gravitational Waves

These lectures, presented at the 2022 TASI summer school, give an introductory overview of first-order phase transitions in the early Universe, baryogenesis, and the resulting gravitational wave phenomenology. We introduce thermal field theory via the imaginary time formalism, and comment on the pitfalls of 1-loop calculations and alternative approaches. Then, we discuss how to calculate the false vacuum decay rate in first order phase transitions, of which we give various examples in theories beyond the Standard Model. Baryogenesis is presented via the Sakharov conditions, and how they are met in important classes of examples. Finally, we explore gravitational waves from the early Universe, first reviewing the basics of gravitational wave generation and then focusing on the specific example of first order phase transitions.