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arXiv · 1903.11428

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

S. X. Tian·Zong-Hong Zhu
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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.

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S. X. Tian, Zong-Hong Zhu. 2019-03-27. Newtonian approximation and possible time-varying $G$ in nonlocal gravities. https://doi.org/10.1103/physrevd.99.064044

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