Fate of false vacuum in non-perturbative regimes: Gravity effects

A formalism to describe the false-vacuum decay in non-perturbative regimes was proposed recently. Here, we extend it to the presence of Einstein gravity and calculate the corresponding effective potential and decay rate for a $\lambda \phi^4$ scalar field theory. A comparison with the usual perturbative decay rate shows that the higher the coupling $\lambda$, the greater the decay probability. From the running of the self-interaction coupling, we conclude that the theory becomes weakly coupled in the infrared limit, which proves that Einstein gravity made the weak coupling approximation even more reliable as the universe cooled down. We comment on future applications of these results to cosmological phase transitions, gravitational-wave astronomy, and condensed matter systems.