Jun Wang, Ya-Bo Wu, Yong-Xin Guo, Wei-Qiang Yang, Lei Wang
The energy conditions and the Dolgov-Kawasaki criterion in generalized $f(R)$ gravity with arbitrary coupling between matter and geometry are derived in this paper, which are quite general and can degenerate to the well-known energy conditions in GR and $f(R)$ gravity with non-minimal coupling and non-coupling as special cases. In order to get some insight on the meaning of these energy conditions and the Dolgov- Kawasaki criterion, we apply them to a class of models in the FRW cosmology and give some corresponding results.
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http://arxiv.org/abs/1212.4921
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