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In the theories of generalized modified gravity, the acceleration equation isgenerally fourth order. So it is hard to analyze the evolution of the Universe.In this paper, we present a class of generalized modified gravity theorieswhich have the acceleration equation of second order derivative. Then both thecosmic evolution and the weak-field limit of the theories are easilyinvestigated. We find that not only the Big-bang singularity problem but alsothe current cosmic acceleration problem could be easily dealt with.

Generalized modified gravity with the second order acceleration equation