Chromo-Natural Inflation: Natural inflation on a steep potential with
  classical non-Abelian gauge fields
  We propose a model for inflation consisting of an axionic scalar field
coupled to a set of three non-Abelian gauge fields. Our model's novel
requirement is that the gauge fields begin inflation with a rotationally
invariant vacuum expectation value (VEV) that is preserved through
identification of SU(2) gauge invariance with rotations in three dimensions.
The gauge VEV interacts with the background value of the axion, leading to an
attractor solution that exhibits slow roll inflation even when the axion decay
constant has a natural value ($<M_{\rm Pl}$). Assuming a sinusoidal potential
for the axion, we find that inflation continues until the axionic potential
vanishes. The speed at which the axion moves along its potential is modulated
by its interactions with the gauge VEV, rather than being determined by the
slope of its bare potential. For sub-Plankian axion decay constants vanishingly
small tensor to scalar ratios are predicted, a direct consequence of the Lyth
bound. The parameter that controls the interaction strength between the axion
and the gauge fields requires a technically natural tuning of
$\mathcal{O}$(100).
