Gravitational effects in vacuum decay

In my presentation I will mainly concentrate on two aspects of
metastable vacuum decay with gravity:
1. The possibility of wormholes creation as a result of quantum tunneling
in theories with non-minimal coupling to gravity  and
2. Negative mode problem, which is in the existence of infinitely many
eigenstates with negative eigenvalues in the spectrum of linear perturbations
about some bounce solutions describing vacuum decay.
I plan to review this problem briefly and discuss its current status.