Power-law Bianchi type I inflation with multiple vector fields

We investigate an inflationary anisotropic universe in a supergravity-motivated model with one scalar field non-minimally coupled to multiple vector fields. We restrict ourselves to the Bianchi type I metric, which describes a homogeneous but anisotropic universe. For consistency, we consider a configuration consisting of one homogeneous scalar field and three mutually orthogonal vector fields. As a result, we find four types of power-law solutions, classified according to the number of non-vanishing vector fields. Moreover, we show that all these solutions are stable under certain conditions on the model parameters, thereby defining stability regions described both quantitatively and qualitatively. Interestingly, our analysis suggests that vector fields with significantly larger coupling constants tend to persist as the universe expands, while those with significantly smaller coupling constants are eventually diluted. On the other hand, we also find that the anisotropies depend on the number of persisting vector fields. Furthermore, our claims are confirmed by numerical calculations. This work may therefore shed light on how vector fields and anisotropies evolve in an inflationary universe.