Non-conformal obstructions to bubble expansion

Abstract

We investigate the hydrodynamics of expanding bubbles in first-order phase transitions with non-conformal thermodynamics. We analyze a broad class of equations of state interpolating between bag-model descriptions, commonly used for electroweak transitions, and QCD-like theories. As a concrete benchmark, we determine the bubble solutions for pure SU(3) Yang-Mills theory. We uncover a new set of hydrodynamic obstructions to bubble expansion. These obstructions arise both at the bubble wall and along the fluid flow, and can partially or completely eliminate otherwise allowed solutions. We also identify a new class of solutions, which we dub "shocked detonations", consisting of ordinary detonations with an additional shock inserted in the rarefaction wave. As a consequence of these obstructions, the space of admissible bubble wall velocities is significantly constrained, with gaps appearing between different expansion regimes. For example, for QCD-like theories, all detonation solutions, including shocked detonations, are excluded. We show that these effects can strongly impact the kinetic energy budget of the fluid and, therefore, the resulting gravitational-wave signal, potentially suppressing the most efficient configurations. Our results highlight the importance of non-conformal dynamics for accurately modeling phase transitions and the resulting gravitational-wave spectrum. The code used to construct the bubble solutions is publicly available. For completeness, we also show how the interpolation between the bag-model and QCD-like limits can be realized holographically by varying the backreaction of matter fields on the geometry.