Nonlocal Gravity: Modification of Newtonian Gravitational Force in the Solar System

Abstract

Nonlocal gravity (NLG) is a classical nonlocal generalization of Einstein’s theory of gravitation developed in close analogy with the nonlocal electrodynamics of media. It appears that the nonlocal aspect of the universal gravitational interaction could simulate dark matter. Within the Newtonian regime of NLG, we investigate the deviation of the gravitational force from the Newtonian inverse square law as a consequence of the existence of the effective dark matter. In particular, we work out the magnitude of this deviation in the solar system out to 100 astronomical units. Moreover, we give an improved lower limit for the short-range parameter of the reciprocal kernel of NLG.

Anisotropic Cosmology in the Local Limit of Nonlocal Gravity

“…Linearized NLG has been investigated in detail [4]. Within the Newtonian regime of NLG, it appears possible to account for the rotation curves of nearby spiral galaxies as well as for the solar system data [27][28][29][30][31]. Beyond the linear domain, no exact solution is known except for the trivial result that in the absence of gravity we have Minkowski spacetime [26].…”

“…Nonlocal gravity, in its Newtonian regime, simulates dark matter. It is therefore possible to account for the gravitational effects in the solar system as well as in nearby galaxies and clusters of galaxies [27][28][29][30][31]. A comprehensive account of these studies is contained in [4].…”

Nonlocal Gravity: Fundamental Tetrads and Constitutive Relations

“…Similarly, as illustrated by Equations ( 35) and (36), the 16 field equations of NLG for the 16 components of the fundamental tetrad e µ α naturally split into 10 nonlocally modified equations of GR plus 6 integral constraint equations for the nonlocality tensor N µνρ . These constraints disappear in the Newtonian regime of NLG, while the nonlocal modification of GR has the interpretation of effective dark matter [1,[19][20][21][22][23].…”

“…Observational data regarding nearby spiral galaxies and clusters of galaxies are consistent with [19] µ 0 = 0.059 ± 0.028 kpc −1 , 0 ≈ 3 ± 2 kpc . (A18) Finally, solar system data provide a lower bound for a 0 , namely, a 0 10 15 cm [20,23].…”

Local Limit of Nonlocal Gravity: Cosmological Perturbations

“…) ¢ must be ultimately determined by observation. In this connection, linearized NLG has been treated in detail in Mashhoon (2017) and the Newtonian regime of the theory has been compared with observational data (Rahvar & Mashhoon 2014;Chicone & Mashhoon 2016;Roshan & Mashhoon 2021, 2022a, 2022b. Within the nonlinear regime of NLG, it has been possible to show that de Sitter spacetime is not an exact solution (Mashhoon 2022); indeed, the only known exact solution of NLG is the trivial solution, namely, we find the Minkowski spacetime in the absence of gravitation.…”