Vacuum Bubbles in the Presence of a Relativistic Fluid

TL;DR

This work investigates how vacuum bubbles from first-order cosmological phase transitions evolve when the order parameter is coupled to a relativistic fluid. It develops a relativistic fluid–scalar-field framework with a phenomenological coupling and studies bubble nucleation and evolution across three strength regimes (α values) using high-resolution lattice simulations. The key finding is that fluid coupling slows bubble-wall velocities and disrupts the idealized SO(3,1) symmetry, highlighting significant field–fluid energy exchange and the potential impact on gravitational-wave production. The study provides a robust numerical platform applicable to a broad range of scales and lays the groundwork for connecting microphysical parameters to observable cosmological signals.

Abstract

First order phase transitions are characterized by the nucleation and evolution of bubbles. The dynamics of cosmological vacuum bubbles, where the order parameter is independent of other degrees of freedom, are well known; more realistic phase transitions in which the order parameter interacts with the other constituents of the Universe is in its infancy. Here we present high-resolution lattice simulations that explore the dynamics of bubble evolution in which the order parameter is coupled to a relativistic fluid. We use a generic, toy potential, that can mimic physics from the GUT scale to the electroweak scale.

Figures (4)

• Figure 1: The unit-less potential, $\bar{V}(\psi)$, for different values of $\alpha$. We cut off the $\alpha=0.45$ curve to retain some details of the curves for higher values of $\alpha$.
• Figure 2: The instanton profiles for different values of $\alpha$. Field values are rescaled by the difference in field values in the minima, equivalent to the field values in the true vacuum, $\psi_{-}$.
• Figure 3: The field profile, $\psi$, radial fluid velocity, $v$, and energy density profile, $\ln(\bar{\epsilon})$, for various coupling strengths (identified to the left of each set of plots) and potential differences: (a) Case I ($\alpha=0.96$), (b) Case II ($\alpha=0.65$) and (c) Case III ($\alpha = 0.45$). Grey horizontal lines in the field profile plots represent field values associated with the local extrema (the upper line in each plot is the maximum of the potential and the lower line is the true vacuum). Horizontally these plots correspond to times when the radius of an uncoupled bubble reaches $\bar{R} = 0$, $\bar{R}=1.5\bar{R}_0$, and $\bar{R} = 2\bar{R}_0$.
• Figure 4: Plots of the relativistic $\gamma$-factor of the bubble wall as a function of radius (top), and relative bubble wall velocities as a function of radius (bottom).