I'm reading this review right now. The claim seems to be that when you have an expanding "false vacuum", finite size bubbles form due to phase transition (cause by finite action instantons) (which, in itself might then evolve, etc). My questions is, if I imagine these bubbles to be moving away from each other due to exponential expansion of the false vacuum, then how will they come near each other and collide?
The size of these bubbles is growing nearly by the speed of light. So if the boundaries of two such bubbles are close enough to each other, the exponential expansion of the parent space in between them, even if this expansion exists, is negligible relatively to the shrinking distance between the bubbles due to their growth. That's why the bubbles collide after a finite time.
Of course, if the bubbles are far enough, e.g. (or i.e.) behind the horizons of each other, their growth isn't enough to overcome the exponentially growing separation and they cannot collide.