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In this study, we generalize the work of Farhi, Guth and Guven [Nucl. Phys. B339 (1990) 417] to include a wormhole effect. We study the influence of thewormhole on the tunneling of the false vacuum bubble. The spherically symmetricbubble has two domain walls. The classical dynamics of each domain wall areconstrained by two classically forbidden regions. We find that the wormhole hasincreased the number of instantons and thus can enhance the tunneling rate. Wehave analytically derived the formula for the bubble tunneling rate, which isconsistent with the result obtained by Farhi, Guth and Guven when the wormholedisappears. We show that the tunneling rate increases with the throat radius ofthe wormhole. Furthermore, we illustrate that the tunneling rate increases withan increases in the mass of the black hole or the surface tension. In the casewhere a wormhole exists within a bubble and is connected to another universe,we demonstrate that the bubble can enter into another universe through quantumtunneling.

Wormhole influence on the false vacuum bubble tunneling