  Some solutions describing vacuum decay exhibit a catastrophic instability.
This, so-called negative mode problem in quantum tunneling with gravity, was
discovered 34 years ago and in spite of the fact that in these years many
different groups worked on this topic, it has still not been resolved. Here, we
briefly summarize the current status of the problem and investigate properties
of the bounces, numerically and analytically for physically interesting
potentials. In the framework of the Hamiltonian approach we show that for
generic polynomial potentials the negative mode problem could arise at energies
much lower than the Planck mass, indicating that the negative mode problem is
not related to physics at the Planck scale. At the same time we find that for a
Higgs like potential, as it appears in the standard model, the problem does not
appear at realistic values of the potential's parameters but only at the Planck
scale.
