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

TL;DR

This paper derives exact formulas for gravitational potentials in open and closed universes, showing how spatial curvature influences gravitational forces and has implications for astrophysical object motion and large-scale structure formation.

Contribution

It provides new exact formulas for gravitational potentials considering spatial curvature, highlighting their effects on forces and astrophysical dynamics.

Findings

In open universe, gravitational force is exponentially suppressed at large distances.

In closed universe, the force from a mass is zero at the antipodal point.

Formulas are applicable for modeling galaxy motion and structure formation.

Abstract

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