Inflationary dynamics with a non-Abelian gauge field

We study the dynamics of the homogeneous and isotropic universe with a scalar field and an SU(2) non-Abelian gauge (Yang-Mills) field. The scalar field has an exponential potential and the Yang-Mills field is coupled to the scalar field with an exponential function of the scalar field. We find that the magnetic component of the Yang-Mills field assists acceleration of the cosmic expansion and a power-law inflation becomes possible even if the scalar field potential is steep, which may be expected from some compactification of higher-dimensional unified theories of fundamental interactions. This power-law inflationary solution is a stable attractor in a certain range of coupling parameters. Unlike the case with multiple Abelian gauge fields, the power-law inflationary solution with the dominant electric component is unstable because of the existence of nonlinear coupling of the Yang-Mills field. We also analyze the dynamics for the noninflationary regime, and find several attractor solutions.