New constraints on axion-gauge field dynamics during inflation from $Planck$ and BICEP/Keck data sets

We present new constraints on spectator axion-${\rm U}(1)$ gauge field interactions during inflation using the latest $Planck$ (PR4) and BICEP/Keck 2018 data releases. This model can source tensor perturbations from amplified gauge field fluctuations, driven by an axion rolling for a few e-folds during inflation. The gravitational waves sourced in this way have a strongly scale-dependent (and chiral) spectrum, with potentially visible contributions to large/intermediate scale $B$-modes of the CMB. We first derive theoretical bounds on the model imposing validity of the perturbative regime and negligible backreaction of the gauge field on the background dynamics. Then, we determine bounds from current CMB observations, adopting a frequentist profile likelihood approach. We study the behaviour of constraints for typical choices of the model's parameters, analyzing the impact of different dataset combinations. We find that observational bounds are competitive with theoretical ones and together they exclude a significant portion of the model's parameter space. We argue that the parameter space still remains large and interesting for future CMB experiments targeting large/intermediate scales $B$-modes.