  Axion-inflation models are a compelling candidate as a mechanism behind the
accelerated expansion in the early universe in light of the possibility to
embed them in higher dimensional UV complete theories and the exciting prospect
of testing them with next-generation cosmological probes. Adding an Abelian
gauge sector to axion-inflation models makes for a rich, interesting,
phenomenology spanning from primordial black holes to gravitational waves
(GWs). Several recent studies employ an approximate analytic (Gaussian)
template to characterize the effect of gauge field production on cosmological
perturbations. In this work we go beyond such approximation and numerically
study particle production and the ensuing scalar and tensor spectra. We find a
significant deviation from results based on log-normally distributed vector
field excitations. As an important phenomenological application of the improved
method, we study the expected chirality and spectral index of the sourced GW
background at scales relevant for current and next-generation GW detectors. One
striking feature is that of a scale-dependent chirality. We derive a
consistency relation between these two observables that can serve as an
important tool in identifying key signatures of multi-field dynamics in axion
inflation.
