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

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.

arXiv commentv2 (matching the publication in European Physical Journal C) = v1 + minor changes + new Refs.; 8 pages, 3 figures

References in corpus (14)

• Observational constraints on the tilted spatially-flat and the untilted nonflat $\varphi$CDM dynamical dark energy inflation models
• Metric Tests for Curvature from Weak Lensing and Baryon Acoustic Oscillations
• Observational constraints on the tilted flat-XCDM and the untilted nonflat XCDM dynamical dark energy inflation parameterizations
• First-order Cosmological Perturbations Engendered by Point-like Masses
• Remarks on mechanical approach to observable Universe
• Hubble flows and gravitational potentials in observable Universe
• Rigorous theoretical constraint on constant negative EoS parameter $\omega$ and its effect for the late Universe
• Cosmic screening of the gravitational interaction
• Scalar and vector perturbations in a universe with discrete and continuous matter sources
• Second-order Cosmological Perturbations Engendered by Point-like Masses
• Perfect fluids with $\omega =\mathrm{const}$ as sources of scalar cosmological perturbations
• Cosmological law of universal gravitation
• Zero average values of cosmological perturbations as an indispensable condition for the theory and simulations
• Analytic expressions for the second-order scalar perturbations in the $\Lambda$CDM Universe within the cosmic screening approach

Cited by in corpus (12)

• The galaxy power spectrum take on spatial curvature and cosmic concordance
• Using quasar X-ray and UV flux measurements to constrain cosmological model parameters
• Quasar X-ray and UV flux, baryon acoustic oscillation, and Hubble parameter measurement constraints on cosmological model parameters
• Constraints on cosmological parameters from gamma-ray burst peak photon energy and bolometric fluence measurements and other data
• Using SPTpol, Planck 2015, and non-CMB data to constrain tilted spatially-flat and untilted non-flat $\Lambda$CDM, XCDM, and $\varphi$CDM dark energy inflation cosmologies
• Duel of cosmological screening lengths
• Gravitational potential in spherical topologies
• Cosmic curvature on large-scale structures with homogeneous dark energy
• Effect of the spatial curvature on light bending and time delay in curved Einstein-Straus--de Sitter spacetime
• Scalar and vector perturbations in a universe with nonlinear perfect fluid
• Cosmological Perturbations Engendered by Discrete Relativistic Species
• Effect of peculiar velocities of inhomogeneities on the shape of gravitational potential in spatially curved universe