Stability analysis of inflation with an SU(2) gauge field
  We study anisotropic cosmologies of a scalar field interacting with an SU(2)
gauge field via a gauge-kinetic coupling. We analyze Bianchi class A models,
which include Bianchi type I, II, VI0, VII0, VIII and IX. The linear stability
of isotropic inflationary solution with background magnetic field is shown,
which generalizes the known results for U(1) gauge fields. We also study
anisotropic inflationary solutions, all of which turn out to be unstable. Then
nonlinear stability for the isotropic inflationary solution is examined by
numerically investigating the dependence of the late-time behaviour on the
initial conditions. We present a number of novel features that may well affect
physical predictions and viability of the models. First, in the absence of
spatial curvature, strong initial anisotropy leads to a rapid oscillation of
gauge field, thwarting convergence to the inflationary attractor. Secondly, the
inclusion of spatial curvature destabilizes the oscillatory attractor and the
global stability of the isotropic inflation with gauge field is restored.
Finally, based on the numerical evidence combined with the knowledge of the
eigenvalues for various inflationary solutions, we give a generic lower-bound
for the duration of transient anisotropic inflation, which is inversely
proportional to the slow-roll parameter.
