On principle of inertia in closed universe

If our universe is asymptotic to a de Sitter space, it should be closed with curvature in O(Λ) in view of dS special relativity. Conversely, its evolution can fix on Beltrami systems of inertia in the ds-space without Einstein's 'argument in a circle'. Gravity should be local ds-invariant based on localization of the principle of inertia.