Dynamics of inflation with mutually orthogonal vector fields in a closed universe

We study the dynamics of a homogeneous, isotropic, and positively curved universe in presence SU(2) gauge field or triplet mutually orthogonal vector fields. In case we use previously known ansatz for gauge-field configuration, but without non-abelian symmetries is more nontrivial develop new ansatz. particular consider axion-SU(2) inflation with fields having U(1)$\times$U(1)$\times$U(1) symmetry, analyze their detail numerically. Novel effects spatial curvature come into play through fields, which causes unconventional pre-inflationary dynamics. It found that closed slightly stable against collapse than filled solely an inflaton field.