axion to a $4$-form [@sol4], modify the axion kinetic term [@sol5], or slow-down the axion through particle production [@sol6a; @sol6b]. In particular, in the mechanism of [@sol6a] the dissipation occurs through the production of a U(1) field coupled to the inflaton $\varphi$ through the interaction $\frac{\varphi}{f} F {\tilde F}$ between the inflaton and an Abelian gauge field. Ref. [@Adshead:2012kp] showed that this coupling can also affect the background evolution (prior to any particle production consideration) if the U(1) field is replaced by a SU(2) field with a nonvanishing vacuum expectation value (vev). Due to the interaction with the vev of the vector multiplet, the inflaton can be in slow roll even if its potential would otherwise (i.e. in absence of this interaction) be too steep to give inflation. As shown in [@Adshead:2012qe; @SheikhJabbari:2012qf], Gauge-flation appears as an analogous (“dual”) version of this mechanism. The Gauge-flation formulation is particularly suggestive since it is characterized by the vector field only. To our knowledge, this is the first and only existing stable model in which inflation is driven by a vector field alone (previously introduced models with dynamical vector fields during inflation either have dynamically relevant scalar fields [@review4], or ghosts [@hcp]).

The 