The Unreasonable Effectiveness of the Tunneling Potential

The Tunneling Potential Formalism was introduced to calculate the tunneling actions that control vacuum decay as an alternative to the standard Euclidean Formalism. The new approach sets the problem as a simple variational problem in field space with decay described by a tunneling potential function Vₜ that extremizes a simple action functional S[Vₜ] and has a number of appealing properties that have been presented elsewhere. In this note I discuss several instances in which this Vₜ approach seems to give more than one would have expected a priori, as the following: the Vₜ describing the decay is a minimum of the new action S[Vₜ] rather than a saddle point; the decay of AdS, dS or Minkowski vacua are governed by a unique universal S[Vₜ] which also gives the Hawking-Moss instanton in the appropriate limit; physically relevant solutions beyond the Coleman-De Luccia (CdL) bounce, like pseudo-bounces or bubbles of nothing (BoNs), show up in a straightforward way as generalizations of the CdL bounce, with the correct boundary conditions; in cases for which the Euclidean action calculation requires the inclusion of particular boundary terms (like for BoNs or for the decay of AdS maxima above the Breitenlohner-Freedman bound) S[Vₜ] gives the correct result without the need of including any boundary term.