Cosmological phase transitions are known to produce a sizable background of gravitational waves (GWs) in the early Universe. This occurs via two main mechanisms: 1) due to the dynamics associated with bubble nucleation during first order transitions, and 2) by the formation and subsequent annihilation of topological defects. After reviewing the underlying particle physics we will discuss the prospects for detecting GWs produced by either mechanism, with focus on the nHz range relevant for Pulsar Timing Arrays. We will then show how bubble nucleation and defect formation can actually exhibit a non-trivial interplay in multi-step phase transitions, with special attention to the electroweak phase transition in scalar extensions of the Standard Model.
