  The shift-symmetric coupling of a pseudo-scalar particle driving inflation to
gauge fields provides a unique way of probing cosmic inflation. We show for an
SU(2) gauge group how a classical isotropic background gauge field develops
from the standard quantum mechanical vacuum in the far past. Over the course of
inflation, the theory dynamically evolves from an approximately abelian regime
into an inherently non-abelian regime, with distinct predictions for the scalar
and tensor power spectra. The latter regime closely resembles a setup known as
chromo-natural inflation, although our main focus here is on a new part of the
parameter space which has received little attention so far. For single-field
slow roll inflation models, large scales may exit the horizon in the abelian
regime, ensuring agreement with the observations of the anisotropies in the
cosmic microwave background, whereas smaller scales experience the non-abelian
effects. This results in a strong enhancement of the stochastic gravitational
wave background at small scales, e.g. at frequencies accessible with
ground-based interferometers. For the scalar power spectrum, a similar
enhancement arises due to non-linear contributions.
