Gauge-flation vs chromo-natural inflation

Gauge-flation, non-Abelian gauge field inflation, which was introduced in Maleknejad and Sheikh-Jabbari (2011) [4] and analyzed more thoroughly in Maleknejad and Sheikh-Jabbari (2011) [5], is a model of inflation driven by non-Abelian gauge fields minimally coupled to Einstein gravity. In this model a certain rotationally invariant combination of gauge fields plays the role of the inflaton. Recently, the chromo-natural inflation model was proposed (Adshead and Wyman, 2012 [8]) which besides the non-Abelian gauge fields also involves an axion field. In this short Letter we show that the model involving axions, indeed allows for various slow-roll trajectories for different values of its parameters: A specific trajectory discussed in Adshead and Wyman (2012) [8] starts from a "small axion" region, while the trajectory considered in Maleknejad and Sheikh-Jabbari (2011) [4,5] corresponds to a "large axion" region.