Evidence for renormalized instantons in real-time simulations of vacuum decay

While vacuum decay is traditionally described by Euclidean instanton methods, lattice simulations enable real-time modeling of dynamical observables relevant to cosmology and upcoming cold-atom analog experiments. We investigate the relationship between these approaches by extracting ensemble-averaged bubble profiles from zero-temperature simulations of a relativistic scalar field. Our observed profiles differ markedly from the bare Coleman bounce and classical thermal predictions. However, we find that instanton solutions in an appropriately renormalized potential reproduce both the measured profiles and their dependence on the UV cutoff, and predict decay rates consistent with simulations across the parameter range considered. The fact that a single renormalized Euclidean object captures these independent observables provides strong evidence that renormalization accounts for the discrepancy between the two formalisms, and establishes a quantitative link between instanton predictions, lattice simulations, and forthcoming empirical tests of vacuum decay.