$\epsilon$ and $r$, respectively), which does not apply in this context, since it holds for a free inflaton and unsourced tensor modes. The stability result (\[cn-instab\]) was later obtained independently by [@Adshead:2013qp], that also presented a complete study of the gravitational waves produced in the model (correcting an error in the original version of [@Dimastrogiovanni:2012ew]), showing that they are chiral. Ref. [@Dimastrogiovanni:2012ew] also presented the scalar and tensor power spectrum of the Chromo-natural inflation for some illustrative choices of the parameters. None of the examples presented in [@Dimastrogiovanni:2012ew] leads to an acceptable phenomenology. In particular, these example showed that the spectrum of the scalar perturbations is too red at small $m_g/H$, while the tensor modes are too high at large $m_g/H$. Based on this, ref. [@Dimastrogiovanni:2012ew] argued that the simultaneous requirements of sufficiently flat scalar spectrum and of sufficiently small tensor mode could pose significant bounds on the model, and potentially rule it out as a model of sub-Planckian $f$. This was later confirmed by [@Adshead:2013nka] through an exhaustive parameter scan in the model.

A study of the perturbations of Gauge-flation can instead be found in [@Maleknejad:2011jw]. Ref. [@Maleknejad:2011jw] concluded that all parameter choices lead to a stable solution (contrary 