First-order phase transitions in the early universe could produce stochastic gravitational wave signals observable at future space-based observatories such as LISA; however, existing methods for predicting these signals are limited to weakly-coupled theories. In this talk, I present a new, nonperturbative formalism for false vacuum decay that integrates over local fluctuations in field space using the functional renormalization group. As I will demonstrate for a simple model, this method opens the door to reliable gravitational wave signal and false vacuum decay rate calculations for a wide range of strongly-interacting theories.