Mass curves spacetime. The relative acceleration of nearby geodesics of free test particles indicates the sign of the spacetime curvature. Convergent geodesics mean positive, divergent negative curvature. But also the metric expansion of space curves spacetime. The geodesics may be convergent or divergent as well depending on whether the universe expands decelerating or accelerating. One could suspect that again convergent means positive and divergent negative curvature of spacetime. Is that true? I have some doubts whether this analogy holds, because Schwarzschild metric is one thing and FRW metric, which describes the expansion of the universe something much different.