The isotropic attractor solution of axion-SU(2) inflation: universal isotropization in Bianchi type-I geometry

SU(2) gauge fields coupled to an axion field can acquire an isotropic background solution during inflation. We study homogeneous but anisotropic inflationary solutions in the presence of such (massless) gauge fields. A gauge field in the cosmological background may pose a threat to spatial isotropy. We show, however, that such models generally isotropize in Bianchi type-I geometry, and the isotropic solution is the attractor. Restricting the setup by adding an axial symmetry, we revisited the numerical analysis presented in [1]. We find that the reported numerical breakdown in the previous analysis is an artifact of parametrization singularity. We use a new parametrization that is well-defined all over the phase space. We show that the system respects the cosmic no-hair conjecture and the anisotropies always dilute away within a few e-folds.

Automated summary

The study investigates isotropic background solutions of SU(2) gauge fields coupled to an axion field during inflation, showing that these models generally isotropize in Bianchi type-I geometry. By adding axial symmetry to the setup and using a new parametrization, the study revisits numerical analysis showing that reported numerical breakdown in the previous analysis was due to parametrization singularity, demonstrating that the system respects the cosmic no-hair conjecture with anisotropies diluting away within a few e-folds.