Abstract
There is a single negative mode in the spectrum of small perturbations about the tunneling solutions describing a metastable vacuum decay in flat spacetime. This mode is needed for consistent description of decay processes. When gravity is included the situation is more complicated. There are different answers in different reduction schemes. An approach based on elimination of scalar field perturbations shows no negative mode, whereas the recent approach based on elimination of gravitational perturbations indicates presence of a negative mode. In this contribution we analyse and compare the present approaches to the negative mode problem in false vacuum decay with gravity.
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