Abstract
In order to constrain f(R, Lm) gravity from theoretical aspects, its energy conditions are derived in this paper. These energy conditions given by us are quite general and can be degenerated to the well-known energy conditions in general relativity and f(R) theories of gravity with arbitrary coupling, non-minimal coupling and non-coupling between matter and geometry, respectively, as special cases. To exemplify how to use these energy conditions to restrict f(R, Lm) gravity, we consider a special model in the FRW cosmology and give some corresponding results by using astronomical observations.
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