Bubble Wall Velocity from Holography

TL;DR

This paper uses holography to calculate the velocity of bubble walls during cosmological phase transitions in a strongly coupled gauge theory, revealing a linear relation with pressure difference and energy density, and confirming hydrodynamics applicability.

Contribution

It introduces a holographic method to compute bubble wall velocity from first principles in a strongly coupled gauge theory, linking velocity to thermodynamic ratios.

Findings

Wall velocity is approximately linearly related to pressure difference over energy density.

The bubble wall profile resembles an equilibrium phase-separated state at the critical temperature.

Ideal hydrodynamics accurately describes the system except near the wall.

Abstract

Cosmological phase transitions proceed via the nucleation of bubbles that subsequently expand and collide. The resulting gravitational wave spectrum depends crucially on the bubble wall velocity. Microscopic calculations of this velocity are challenging even in weakly coupled theories. We use holography to compute the wall velocity from first principles in a strongly coupled, non-Abelian, four-dimensional gauge theory. The wall velocity is determined dynamically in terms of the nucleation temperature. We find an approximately linear relation between the velocity and the ratio $\Delta \mathcal{P}/\mathcal{E}$, with $\Delta \mathcal{P}$ the pressure difference between the inside and the outside of the bubble and $\mathcal{E}$ the energy density outside the bubble. Up to a rescaling, the wall profile is well approximated by that of an equilibrium, phase-separated configuration at the critical temperature. We verify that ideal hydrodynamics provides a good description of the system everywhere except near the wall.