The universe right after the Big Bang was like a boiling cauldron: bubbles of a new state of matter were bursting and growing everywhere. These were first-order phase transitions — exactly like water boiling, only at temperatures reaching trillions of degrees. According to the Standard Model, one such transition could have spawned the very matter that makes up everything around us.
Calculations based on pure Yang–Mills theory (a simplified version of the strong interaction) have revealed an unpleasant surprise. It turns out that the motion of bubble walls hits hydrodynamic barriers — as if a bubble in boiling water suddenly runs into an invisible wall. Some solutions simply vanish. For physics close to quantum chromodynamics, explosive expansion modes — detonations — are completely forbidden. Instead, 'shocked detonations' can arise: an additional shock wave is born inside a rarefaction wave.
All this dramatically changes the energy balance inside the bubbles and, consequently, predictions about the gravitational-wave background. If detonations are forbidden, the most powerful waves simply do not occur. On the other hand, knowing about such invisible barriers helps to better separate extraneous bursts from the sought-after ripples. The code for constructing solutions has been made publicly available — now anyone can check how the bubbles of the early universe conceal their waves.
as written by the authors arXiv:2607.27874v1
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.
The walls of such bubbles can accelerate to nearly the speed of light, but sometimes slow down to the speed of sound — like a speedboat suddenly dropping to a gentle current.