Cosmological thermal first-order phase transitions are assumed to proceed via the nucleation of bubbles and subsequent expansion and collision. The out-of-equilibrium physics involved during the collision of bubbles is expected to emit Gravitational Waves (GW) detectable by future generation interferometers like the Laser Interferometer Space Antenna (LISA). The Standard Model of Particle Physics (SM) as we know it does not exhibit any first order thermal phase transitions, meaning that the detection of such GW would imply the direct observation of new physics beyond the SM. It is for this reason that a good theoretical understanding of the features of the GW spectrum emitted during first order thermal phase transitions, together with an exploration of the possible mechanisms, is crucial. An accurate study of such emission implies knowing out-of-equilibrium properties of the underlying Quantum Field Theory, which is known to be challenging even at weak coupling.
In this thesis we employ the AdS/CFT duality to investigate both equilibrium and out-of-equilibrium features of first-order thermal phase transitions in strongly coupled, four-dimensional gauge theories. We pay special attention to the dynamics of bubbles (expanding, collapsing and critical) and we extract the bubble wall velocity, which is of great relevance for an accurate determination of the GW spectrum. Finally, we study the emission produced by an alternative mechanism in theories with sufficiently suppressed nucleation rates, the spinodal instability.