Anisotropic Inflation with Non-Abelian Gauge Kinetic Function

We study an anisotropic inflation model with a gauge kinetic function for a non-abelian gauge field. We find that, in contrast to abelian models, the anisotropy can be either a prolate or an oblate type, which could lead to a different prediction from abelian models for the statistical anisotropy in the power spectrum of cosmological fluctuations. During a reheating phase, we find chaotic behaviour of the non-abelian gauge field which is caused by the nonlinear self-coupling of the gauge field. We compute a Lyapunov exponent of the chaos which turns out to be uncorrelated with the anisotropy.