  We consider Yang--Mills theory with a compact structure group $G$ on
four-dimensional de Sitter space dS$_4$. Using conformal invariance, we
transform the theory from dS$_4$ to the finite cylinder ${\cal I}\times S^3$,
where ${\cal I}=(-\pi/2, \pi/2)$ and $S^3$ is the round three-sphere. By
considering only bundles $P\to{\cal I}\times S^3$ which are framed over the
temporal boundary $\partial{\cal I}\times S^3$, we introduce additional degrees
of freedom which restrict gauge transformations to be identity on
$\partial{\cal I}\times S^3$. We study the consequences of the framing on the
variation of the action, and on the Yang--Mills equations. This allows for an
infinite-dimensional moduli space of Yang--Mills vacua on dS$_4$. We show that,
in the low-energy limit, when momentum along ${\cal I}$ is much smaller than
along $S^3$, the Yang--Mills dynamics in dS$_4$ is approximated by geodesic
motion in the infinite-dimensional space ${\cal M}_{\rm vac}$ of
gauge-inequivalent Yang--Mills vacua on $S^3$. Since ${\cal M}_{\rm vac}\cong
C^\infty (S^3, G)/G$ is a group manifold, the dynamics is expected to be
integrable.
