Bubble nucleation for flat potential barriers

We have studied false vacuum decay for effective potentials in which the false vacuum is separated from the true vacuum by a "flat" potential barrier. By flat, we mean that, near the top of the barrier, the potential varies quartically, rather than quadratically with the field (to leading order). We have discovered several new types of bubble solutions. One type reduces in the flat space-time limit to the mathematical solution introduced by Lee and Weinberg to describe "tunneling without barriers." Based on our analysis, though, we propose a significantly different interpretation of the curved space solution. We numerically study these solutions (plus the Hawking-Moss solution) for a toy model to examine how the dominant tunneling mode may change as a function of parameters. We propose a variant of the new inflationary scenario based on these results.