Vacuum bubbles from cosmic ripples

Abstract

We investigate vacuum decays in the early Universe in the presence of curvature perturbations. For sufficiently large perturbations associated with over-densities, we find that the bounce solution develops an oscillating middle stage near the bubble wall. For small perturbations, we analytically show within the thin-wall approximation that an over- (under-) density would enhance (suppress) the vacuum decay rate with a smaller (larger) initial bubble radius. By numerically solving for the bounce solutions and evaluating the corresponding Euclidean action, we further confirm this behaviour in thick-wall cases. Our results indicate that over-densities can generically trigger vacuum decay at an earlier moment.

Figures (4)

• Figure 1: An illustrative picture of the motion of a scalar field in Euclidean spacetime, where the turning point is denoted as $\phi_0$. The left panel shows a simple rolling from $\phi_0$ to $\phi_F$, which corresponds to a "bubble wall" configuration. The right panel shows the existence of an oscillating middle stage by allowing the friction term to vary in sign.
• Figure 2: The bounce solution under curvature perturbation $\zeta=\mu \exp(-r^2)$ with $\mu=1$ (left), $2$ (middle), and $3$ (right), respectively, where the potential barrier parameter is set to be $\lambda=50$. In the left panel, the condition $r^{-1}+\zeta'$ is always satisfied, and hence there is a bubble wall connecting the two vacuums, while the right two panels exhibit an oscillating middle stage.
• Figure 3: Numerical results of the bounce solutions under different curvature perturbation profiles with $\zeta=0$, $\mu\exp(-r^2)$, $\mu\mathrm{sinc}(\pi r)$, $-\mu\exp(-r^2)$, and $-\mu\mathrm{sinc}(\pi r)$, for $\mu=1/2$, from top to bottom, respectively. Each column corresponds to a different temperature with $\beta=\infty$, $6.5$, $4.5$, and $0$, from left to right, respectively.
• Figure 4: the ratio of the Euclidean action with curvature perturbations to that in the flat case as a function of inverse temperature $\beta=1/T$, with $\mu=1/2$ corresponding to the examples shown in Fig. \ref{['fig: 2D solution']}.