Future gravitational wave interferometers may provide the first direct probe of the first second of our Universe. A first order phase transition in the early Universe would have sourced a stochastic gravitational wave background (SGWB). However, existing methods used to predict this SGWB are limited to weakly-coupled theories and often plagued by large uncertainties. In this talk, I will motivate that some of these obstacles can be overcome through an alternate definition of the action which has a natural implementation in the functional renormalization group. I will demonstrate how the proposal works in a toy model example, and sketch a roadmap towards accurate gravitational phenomenology and other applications.