  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 gauge-field perturbations while keeping the metric
frozen, by diagonalizing the (time-dependent) Yang-Mills 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.
