Can the universe be matter-dominated after a supercooled first-order phase transition?

Abstract

We show that the answer is generally no, at least not immediately. Bubble collisions leave behind a highly inhomogeneous scalar field with persistent relativistic gradients, producing an equation of state between matter and radiation. Using lattice simulations in one, two and three spatial dimensions, we find that the equation of state is controlled by the wall Lorentz factor at collision $γ_\star$: walls with larger $γ_\star$ populate higher-momentum modes and drive the fluid closer to radiation. Matter domination begins only after these modes redshift, at $a/a_\star \simeq γ_\star$, or after the field thermalises through self-scattering and number-changing processes. This delay has direct implications for gravitational waves, primordial black holes and dark matter production.