On Bubble Growth and Droplet Decay in Cosmological Phase Transitions

TL;DR

The paper investigates bubble growth and quark droplet decay during a first-order cosmological phase transition using a spherically symmetric hydro-model that couples hydrodynamics to an order-parameter field. It resolves a finite-width phase boundary and includes surface tension, enabling realistic wall dynamics and the computation of wall velocities through a dissipative coupling $\eta$. The authors verify three hydrodynamic growth modes—weak deflagrations, Jouguet deflagrations, and weak detonations—and show how transitions between them can involve velocity jumps or coexistence of solution branches for the same $\eta$. In the droplet decay study they find no global rarefaction wave behind the evaporating droplet, implying that baryon-number inhomogeneities established earlier are not washed out by late-stage hydrodynamics, though radiative transfer and wall-baryon suppression not included here could alter this conclusion.

Abstract

We study spherically symmetric bubble growth and droplet decay in first order cosmological phase transitions, using a numerical code including both the complete hydrodynamics of the problem and a phenomenological model for the microscopic entropy producing mechanism at the phase transition surface. The small-scale effects of finite wall width and surface tension are thus consistently incorporated. We verify the existence of the different hydrodynamical growth modes proposed recently and investigate the problem of a decaying quark droplet in the QCD phase transition. We find that the decaying droplet leaves behind no rarefaction wave, so that any baryon number inhomogeneity generated previously should survive the decay.

Figures (11)

• Figure 1: The velocity profile approaches the similarity solution as the bubble grows. This run is for $\eta = 1.0T_c$. The time interval between the dashed curves is $\Delta t = 158.75 T_c^{-1}$, and between the solid curves $\Delta t = 675 T_c^{-1}$. The horizontal axis is $\xi \equiv r/t$, distance scaled with time.
• Figure 2: A sequence of velocity profiles for bubbles with different values of $\eta$ (given in units of $T_c$ next to each profile). These profiles are from our hydrodynamical runs. Compare with Fig. 3 of KL, where the profiles are solutions of eqs. (\ref{['veq']}) and (\ref{['Teq']}) (with a bag equation of state).
• Figure 3: The bubble wall velocity and the shock velocity as a function of $\eta$.
• Figure 4: The energy density, velocity, and order parameter profiles for the three different solution classes. The first (a) is a weak deflagration, the second (b) a Jouguet deflagration, and the third (c) a weak detonation.
• Figure 5: A bubble ($\eta = 0.1207T_c$) which first goes to a detonation configuration before settling to a deflagration. The three profiles are from times $t_1 = 1350T_c^{-1}$, $t_2 = 2700T_c^{-1}$, and $t_3 = 10800T_c^{-1}$.