difference emerged in the literature between the perturbations in the two models is a clear indication that a non-negligible difference between the two models must appear when $\varphi$ is accurately integrated out.

It is interesting to understand how precisely this difference emerges, as this may provide some general indication on how accurate one needs to be in integrating out fields from a model of inflation, and still obtain an accurate effective description. This was the main motivation for the present study. As a byproduct, we also deemed useful to update the phenomenological limits on Gauge-flation in the light of the new Planck results [@Ade:2013zuv], particularly if the analogy with Chromo-natural inflation turns out to be accurate also at the perturbative level. To understand this, we computed the cosmological perturbations of Gauge-flation, employing an analogous procedure to the one that we used to study the perturbations of Chromo-natural inflation [@Dimastrogiovanni:2012ew]. Disregarding the vector perturbations (as we realized that considering them would not impact our conclusions) the model has two physical scalar perturbations, two physical left-handed tensor perturbations, and two physical right-handed perturbations. These three groups are decoupled from each other at the linearized level, and each of them is described by 