  We consider here natural inflation in the low energy (two-derivative)
metric-affine theory containing only the minimal degrees of freedom in the
inflationary sector, i.e. the massless graviton and the pseudo-Nambu-Goldstone
boson (PNGB). This theory contains the Ricci-like and parity-odd Holst
invariants together with non-minimal couplings between the PNGB and the
above-mentioned invariants. The Palatini and Einstein-Cartan realizations of
natural inflation are particular cases of our construction. Explicit models of
this type featuring non-minimal couplings are shown to emerge from the
microscopic dynamics of a QCD-like theory with an either sub-Planckian or
trans-Planckian confining scale and that is renormalizable on Minkowski
spacetime. Moreover, for these models, we find regions of the parameter space
where the inflationary predictions agree with the most recent observations at
the $2\sigma$ level. We find that in order to enter the $1\sigma$ region it is
necessary (and sufficient) to have a finite value of the Barbero-Immirzi
parameter and a sizable non-minimal coupling between the inflaton and the Holst
invariant (with sign opposite to the Barbero-Immirzi parameter). Indeed, in
this case the potential of the canonically normalized inflaton develops a
plateau as shown analytically.
