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Within the cosmic screening approach, we obtain the exact formulas for thevelocity-independent gravitational potentials produced by matter in the form ofdiscrete sources distributed in the open and closed Universes. These formulasdemonstrate that spatial curvature of the Universe considerably affect the formof the potentials and forces. While in the open Universe the gravitationalforce undergoes exponential suppression at cosmological distances, in theclosed Universe the force induced by an individual mass is equal to zero at theantipodal point with respect to this mass. The derived formulas are applicablefor investigations of the motion of astrophysical objects (e.g., galaxies) inthe open and closed Universes, and for simulations of the large scale structureformation.

Effect of the spatial curvature of the Universe on the form of the gravitational potential