  A spectator axion-gauge sector, minimally coupled to the inflaton, with the
axion experiencing a momentary stage of fast roll during cosmological
inflation, can generate unique signatures in primordial density fluctuations
and the gravitational wave background. We present the first lattice simulation
of this system using a novel hybrid numerical scheme. This approach solves the
fully nonlinear dynamics of the axion-gauge sector while treating the
gravitational interaction between the axion and inflaton linearly. Initially,
we test the validity of the WKB approximation in the linear regime. We then
investigate strong backreaction dynamics within the axion-gauge sector. Our
findings reveal that backreaction significantly suppresses the growth of the
gauge field and the amplitude of scalar perturbations. The simulation also
allows us to analyze the non-Gaussianity of scalar fluctuations, including
higher-order statistics. We show that, although non-Gaussianity is suppressed
by strong backreaction, it remains higher than in the minimal model where the
axion coincides with the inflaton. Our results highlight the need for
simulations to make robust predictions to test against data from gravitational
wave interferometers and large-scale structure surveys.
