Newtonian approximation and possible time-varying $G$ in nonlocal gravities

Abstract

The Newtonian approximation with a nonvanishing nonlocal background field is analyzed for the scalar-tensor nonlocal gravity and nonlocal Gauss-Bonnet gravity. For these two theories, our calculations show that the Newtonian gravitational constant $G$ is time-varying and $|\dot{G}/G|=\mathcal{O}(H_0)$ for the general case of cosmological background evolution, which is similar to the results of the Deser-Woodard and Maggiore-Mancarella theories. Therefore, observations about the orbit period of binary star (or star-planet) systems could rule out these theories. One thing worth mentioning is that the nonlocal Gauss-Bonnet gravity gives $\Psi =\Phi$ and a constant $G$ in the de Sitter phase. Our results also highlight the uniqueness of the RT model [M. Maggiore, \href{http://dx.doi.org/10.1103/PhysRevD.89.043008}{Phys. Rev. D {\bf 89}, 043008 (2014)}], which is the only nonlocal gravity theory that can successfully describe the gravitational phenomena from solar system to cosmological scales for now.

arXiv comment6 pages, version published in PRD

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• Time evolution of the local gravitational parameters and gravitational wave polarizations in a relativistic MOND theory
• Structure formation in the new Deser-Woodard nonlocal gravity model
• Blackhole in Nonlocal Gravity: Comparing Metric from Newmann-Janis Algorithm with Slowly Rotating Solution
• Revisiting scalar and tensor perturbations in a nonlocal gravity
• On the impact of non-local gravity on compact stars
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