The paper investigates the nonlinear dynamics of a spectator axion-gauge sector during cosmological inflation, where the axion experiences a brief period of fast roll. This system can generate unique signatures in primordial density fluctuations and gravitational wave (GW) backgrounds. The authors present the first lattice simulation of this system using a novel hybrid numerical scheme that solves the fully nonlinear dynamics of the axion-gauge sector while treating the gravitational interaction linearly. They first test the validity of the WKB approximation in the linear regime and then explore strong backreaction dynamics within the axion-gauge sector. The findings reveal that strong backreaction significantly suppresses the growth of the gauge field and the amplitude of scalar perturbations. The simulation also allows for the analysis of non-Gaussianity in scalar fluctuations, showing that it remains higher than in the minimal model where the axion coincides with the inflaton. The results highlight the need for robust simulations to test against data from GW interferometers and large-scale structure surveys.The paper investigates the nonlinear dynamics of a spectator axion-gauge sector during cosmological inflation, where the axion experiences a brief period of fast roll. This system can generate unique signatures in primordial density fluctuations and gravitational wave (GW) backgrounds. The authors present the first lattice simulation of this system using a novel hybrid numerical scheme that solves the fully nonlinear dynamics of the axion-gauge sector while treating the gravitational interaction linearly. They first test the validity of the WKB approximation in the linear regime and then explore strong backreaction dynamics within the axion-gauge sector. The findings reveal that strong backreaction significantly suppresses the growth of the gauge field and the amplitude of scalar perturbations. The simulation also allows for the analysis of non-Gaussianity in scalar fluctuations, showing that it remains higher than in the minimal model where the axion coincides with the inflaton. The results highlight the need for robust simulations to test against data from GW interferometers and large-scale structure surveys.