Gravitational constant in f(R) theories of gravity with non-minimal coupling between matter and geometry☆☆Supported by the National Natural Science Foundation of China under Grant No 11647079, the Scientific Research Foundation of Education Department of Yunnan Province under Grant No 2016ZZX011, the Key Laboratory of Astroparticle Physics of Yunnan Province, and the Donglu Youth Teacher Plan of Yunnan University.

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We study the effect of the non-minimal coupling between matter and geometry on the gravitational constant in the context of f(R) theories of gravity on cosmic scales. For a class of f(R) models, the result shows that the value of the gravitational constant not only changes over time but also has the dampened oscillation behavior. Compared with the result of the standard ΛCDM model, the consequence suggests that the coupling between matter and geometry should be weak.