  We consider vacuum decay in the presence of a non-minimal coupling to
gravity. We extend the usual thin-wall solution to include the non-minimal
coupling. We also perform a full numerical study and discuss the validity of
the new thin-wall approximation. Implications of a large cosmological constant,
whose influence on the geometry boosts the tunnelling rate, are discussed. Our
results show that the influence of the non-minimal coupling differs
significantly between the cases of Minkowski and deSitter backgrounds. In the
latter the decay probability quickly decreases when the coupling grows and in
fact the vacuum can be made absolutely stable simply due to introduction of the
non-minimal coupling. In the case of Minkowski background the effect is much
weaker and the decay rate even increases for small values of the non-minimal
coupling.
