How does SU(N)-natural inflation isotropize the Universe?

We study the homogeneous and anisotropic dynamics of pseudoscalar inflation coupled to an SU(N) gauge field. To see how the initially anisotropic universe is isotropized in such an inflation model, we derive the equations to obtain axisymmetric SU(N) gauge field configurations in Bianchi type-I geometry and discuss a method to identify their isotropic subsets which are the candidates of their late-time attractor. Each isotropic solution is characterized by the corresponding SU(2) subalgebra of the SU(N) algebra. It is shown numerically that the isotropic universe is a universal late-time attractor in the case of the SU(3) gauge field. Interestingly, we find that a transition between the two distinct gauge-field configurations characterized by different SU(2) subalgebras can occur during inflation. We clarify the conditions for this to occur. This transition could leave an observable imprint on the cosmic microwave background and the primordial gravitational wave background.

Automated summary

We investigate the dynamics of pseudoscalar inflation coupled to an SU(N) gauge field, focusing on the isotropization of initially anisotropic universe in this inflation model. By deriving the equations for axisymmetric SU(N) gauge field configurations in Bianchi type-I geometry and identifying the isotropic subsets as late-time attractors, we find that the isotropic universe is a universal attractor in the case of SU(3) gauge field. Furthermore, we discover a possible transition between distinct gauge-field configurations characterized by different SU(2) subalgebras during inflation and clarify the conditions for this transition to occur, which could leave observable imprints on the cosmic microwave background and the primordial gravitational wave background.