paper, we study one of these models, namely the recently proposed Gauge-flation model [@Maleknejad:2011jw]. Gauge-flation is a non-Abelian gauge theory minimally coupled to gravity. At the background level, it is characterized by an effective scalar degree of freedom in the form of the vacuum expectation value (vev) of the spatial component of the gauge field. The action for the model reads [@Maleknejad:2011jw] $$\label{oneeq}
S=\int d^{4}x \sqrt{-g}\left[\frac{M_{p}^{2}}{2}R-\frac{1}{4}F_{\mu\nu}^{a}F^{a,\mu\nu}+\frac{\kappa}{96}\left(F_{\mu\nu}^{a}\tilde{F}^{a,\mu\nu}\right)^{2}\right],$$ where $R$ is the Ricci scalar, $F_{\mu\nu}^{a} \equiv \partial_\mu A_\nu^a -  \partial_\nu A_\mu^a - g \epsilon^{abc} A_\mu^b A_\nu^c$ is the field-strength tensor of a SU(2) gauge field with coupling constant $g$, and $\tilde{F}^{a,\mu\nu} \equiv \frac{\epsilon^{\mu\nu\alpha\beta}}{2 \sqrt{-g}} F_{\alpha\beta}^a$ is its dual ($\epsilon^{\mu\nu\alpha\beta}$ is totally anti-symmetric, and $\epsilon^{0123}=1$).

Thanks to its anti-symmetric structure, the last term in (\[oneeq\]) does not introduce more than two time derivatives in the equations of motion, and therefore, for positive $\kappa$, the model is ghost free. [^1] Moreover, the gauge symmetry is not explicitly broken in this model, and there are no problems associated with the longitudinal vector polarizations, which instead destabilize several models of vector fields in cosmology [@hcp].

The model admits an isotropic background solution, with $$\label{gF}
\langle  A_{i}^{a} \rangle={\hat \phi } \left( t \right) \, \delta_{i}^{a}.$$ Further studies 