  Primordial tensor modes can induce Cosmic Microwave Background spectral
distortions during horizon re-entry. We investigate a specific mechanism
proposed for this purpose, characterized by the coupling of an SU(2) gauge
field to an axion undergoing a momentary stage of rapid evolution during
inflation. Examining also the scalar perturbations produced by this model, we
find that spectral distortions from the scalar modes significantly dominate
those arising from the tensors. This holds true also for an earlier version of
the model based on a U(1) gauge field. The scalar-induced distortions might be
observed in future experiments, and the current COBE/FIRAS constraints already
limit the parameter space of these models. Additionally, we find that delaying
the onset of fast roll in the SU(2) scenario (to enhance the modes at the
scales relevant for spectral distortions, while respecting the CMB constraints
at larger scales) poses a greater challenge compared to the U(1) case. We
propose a way to control the axion speed by varying the size of its coupling to
the gauge fields.
