Observational tests of nonlocal gravity: Galaxy rotation curves and clusters of galaxies

Abstract

A classical nonlocal generalization of Einstein's theory of gravitation has recently been developed via the introduction of a scalar causal "constitutive" kernel that must ultimately be determined from observational data. It turns out that the nonlocal aspect of gravity in this theory can simulate dark matter; indeed, in the Newtonian regime of nonlocal gravity, we recover the phenomenological Tohline-Kuhn approach to modified gravity. A simple generalization of the Kuhn kernel in the context of nonlocal general relativity leads to a two-parameter modified Newtonian force law that involves an additional repulsive Yukawa-type interaction. We determine the parameters of our nonlocal kernel by comparing the predictions of the theory with observational data regarding the rotation curves of spiral galaxies. The best-fitting stellar mass-to-light ratio turns out to be in agreement with astrophysical models; moreover, our results are consistent with the Tully-Fisher relation for spiral galaxies.Light deflection in nonlocal gravity is consistent with general relativity at Solar System scales, while beyond galactic scales an enhanced deflection angle is predicted that is compatible with lensing by the effective "dark matter". Furthermore, we extend our results to the internal dynamics of rich clusters of galaxies and show that 2 the dynamical mass of the cluster obtained from nonlocal gravity is consistent with the measured baryonic mass.

Virial Theorem in Nonlocal Newtonian Gravity

“…In fact, we expect that a 0 < λ 0 < µ −1 0 ; moreover, the short-range parameter a 0 and E may be neglected in Equation (1) when dealing with the rotation curves of spiral galaxies and the internal gravitational physics of clusters of galaxies. In this way, α 0 and µ 0 have been tentatively determined from a detailed comparison of nonlocal gravity with observational data [9]:…”

“…We emphasize that only some of the implications of nonlocal gravity theory have thus far been confronted with observation [9,12]. It is also important to mention here that many other approaches to nonlocal gravitation theory exist that are, however, inspired by developments in quantum field theory.…”

“…Dark matter is currently required in astrophysics for explaining the gravitational dynamics of galaxies as well as clusters of galaxies [9], gravitational lensing observations [10] and structure formation in cosmology [13]. We emphasize that only some of the implications of nonlocal gravity theory have thus far been confronted with observation [9,12].…”

“…The deep connection between inertia and gravitation suggests that gravity could be nonlocal as well, and, in nonlocal gravity, the gravitational memory of past events must then be taken into account. Along this line of thought, a classical nonlocal generalization of Einstein's theory of gravitation has recently been developed [2][3][4][5][6][7][8][9][10][11][12][13]. In this theory, the gravitational field is local but satisfies partial integro-differential field equations.…”

“…The short-range parameter a 0 is necessary in dealing with the gravitational physics of the Solar System, globular clusters and isolated dwarf galaxies; however, it may be safely neglected in dealing with larger systems such as clusters of galaxies. When a 0 = 0, q 1 and q 2 reduce to a single kernel q 0 , q 1 = q 2 = q 0 , and the remaining parameters (λ 0 and µ 0 ) have been determined from a comparison of the theory with the astronomical data regarding a sample of 12 spiral galaxies from the THINGS catalog-see reference [9] for a detailed treatment. The results can be expressed, for the sake of convenience, as λ 0 ≈ 3 kpc and µ −1 0 ≈ 17 kpc.…”