  In this study, we generalize the work of Farhi, Guth and Guven [Nucl. Phys. B
339 (1990) 417] to include a wormhole effect. We study the influence of the
wormhole on the tunneling of the false vacuum bubble. The spherically symmetric
bubble has two domain walls. The classical dynamics of each domain wall are
constrained by two classically forbidden regions. We find that the wormhole has
increased the number of instantons and thus can enhance the tunneling rate. We
have analytically derived the formula for the bubble tunneling rate, which is
consistent with the result obtained by Farhi, Guth and Guven when the wormhole
disappears. We show that the tunneling rate increases with the throat radius of
the wormhole. Furthermore, we illustrate that the tunneling rate increases with
an increases in the mass of the black hole or the surface tension. In the case
where a wormhole exists within a bubble and is connected to another universe,
we demonstrate that the bubble can enter into another universe through quantum
tunneling.
