Abstract: Supercooled first-order phase transitions can reshape the thermal history of the Universe. If the scalar field driving the transition is weakly coupled, bubble collisions may be followed by an era of scalar-field domination, which is commonly assumed to behave like matter. Using lattice simulations, I will show that the post-transition equation of state can deviate significantly from matter domination. Bubble collisions leave behind an inhomogeneous scalar field with persistent relativistic gradients, and the resulting equation of state lies between that of matter and radiation. It is set by the Lorentz factor of the walls at collision, $\gamma_\star$: larger bubble separations lead to more relativistic walls and to a more radiation-like expansion. Matter domination is only recovered once the Universe has expanded by a factor of order $\gamma_\star$, or after the scalar field thermalises through self-scattering and number-changing processes.

This modified expansion history directly affects observables produced during and after the transition. It sets how the gravitational-wave signal is redshifted and diluted before reheating, and hence its amplitude and peak frequency today. It also affects particle production. As an example, I will discuss dark matter production via UV freeze-in during a supercooled transition. In this phase-in regime, the dark matter abundance becomes insensitive to the reheating temperature and instead depends on the details of the transition.