  There exists a small family of analytic SO(4)-invariant but time-dependent
SU(2) Yang-Mills solutions in any conformally flat four-dimensional spacetime.
These might play a role in early-universe cosmology for stabilizing the
symmetric Higgs vacuum. We analyze the linear stability of these "cosmic gauge
fields" against general perturbations, by diagonalizing the (time-dependent)
fluctuation operator around them and applying Floquet theory to its
eigenfrequencies and normal modes. Except for the exactly solvable SO(4)
singlet perturbation, which is found to be marginally stable linearly but
bounded nonlinearly, generic normal modes often grow exponentially due to
resonance effects. Even at very high energies, all cosmic Yang-Mills
backgrounds are rendered linearly unstable.
