Vacuum bubbles from cosmic ripples

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.