Double-layered vacuum bubbles and cosmological phase transitions

Abstract

We investigate the evolution and formation of double-layered vacuum bubbles during cosmological phase transitions with multiple vacua. We employ lattice simulations to show that flyover transitions can produce double-layered vacuum bubbles by overcoming successive potential barriers, thereby suggesting a novel bubble vacuum configuration in cosmological phase transitions. The evolution of these bubbles, including wall acceleration, collisions, and the formation of trapped regions, is explored through numerical simulations. Our results show that the dynamics of double-layered bubbles differ significantly from standard single-wall bubbles, with implications for cosmological observables such as gravitational wave production and baryogenesis.

Figures (6)

• Figure 1: Potential \ref{['eq:potential']} with three minima at $\phi_1$, $\phi_2$ and $\phi_3$. The heights of the two potential barriers are labeled as $V_{b1}$and $V_{b2}$, and the potential differences between the adjacent minima are denoted by $\Delta V_{12}$ and $\Delta V_{23}$.
• Figure 2: Vacuum bubble configuration arising through a quantum tunneling process. The potential parameters are chosen as $\alpha = 0.05$, $\phi_0 = 1.5$, and $\epsilon \phi_0^2= 0.068$. Under these conditions, the scalar field tunnels from the false vacuum into a true vacuum region, forming a bubble with a characteristic profile determined by the bounce solution.
• Figure 3: Numerical simulation results with parameter values $A/A_0 = 1$, $R/R_0=0.8$ and $\alpha=0$ (upper), and $A/A_0 = 1.2$, $R/R_0=1.1$ and $\alpha=0$ (lower), respectively. The comparison illustrates how varying $A$ and $R$ affects the evolution of the scalar field configuration.
• Figure 4: Parameter space where the blue region indicates the absence of a phase transition, the orange region suggests a transition expanding toward the $\phi_2$ vacuum, and the green region indicates a transition to the $\phi_3$ vacuum.
• Figure 5: Dynamics of vacuum decay with $\alpha = 0.035$, $\phi_0 = 1.5$, $A/A_0=7$ and $R/R_0=0.59$ (top), and with $\alpha = -0.038$, $\phi_0 = 1.5$, $A/A_0=11$ and $R/R_0=0.2$ (lower), respectively.