A Scalar One-Loop Benchmark for False-Vacuum Decay and the Expected Number of Bubble Collisions in a Two-Scale Inflation Model

This paper presents a two-scale, single-field potential that admits a metastable de Sitter false vacuum, two degenerate true vacua, and a post-tunneling branch that supports CMB-compatible slow-roll inflation inside nucleated bubbles. Using a flat-space Euclidean bounce and a renormalized scalar one-loop prefactor, the analysis estimates the nucleation rate and the expected number of bubble collisions. We adopt an expected collision number of at least 0.1 as a working criterion for a non-negligible collision abundance. The benchmark shows that a flat-space tunneling solution, successful post-tunneling inflation, and a conditional collision estimate above this threshold can coexist within one potential. A complete prediction for decay in the de Sitter parent vacuum will, however, require a gravitational Coleman–De Luccia calculation and the associated gravitational fluctuations.