Some properties of f(R, L_m) gravity are studied in this paper. Concretely, the energy conditions and the Dolgov–Kawasaki (DK) instability criterion in f(R, L_m) gravity are obtained, which are quite general and can degenerate to the ones in General Relativity (GR) and pure f(R) gravity with non-coupling and non-minimal coupling as well as in [J. Wang and K. Liao, Class. Quantum Grav. 29, 215016 (2012)] as special cases. Furthermore, in order to get some insight on the meaning of the energy conditions and the DK instability criterion, we apply them to the concrete type of f(R, L_m) gravity models and the corresponding constraints on the models are given.

Keywords:

PACS: 98.80.-k, 98.80.Jk, 04.20.-q

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