AdS cycles in eternally inflating background

In the eternally inflating background, the bubbles with AdS vacua will crunch. However, this crunch might be followed by a bounce. It is generally thought that the bubble universe may be cyclic, which will go through a sequence of AdS crunches, until the field inside bubble finally lands at a dS minimum. However, we show that due to the amplification of field fluctuation, the bubble universe going through AdS cycles will inevitably fragment within two or three cycles. We discuss its implication to the eternal inflation scenario.