Conditions and instability in f(R) gravity with non-minimal coupling between matter and geometry

In this paper, on the basis of the generalized f(R) gravity model with arbitrary coupling between geometry and matter, four classes of f(R) gravity models with non-minimal coupling between geometry and matter will be studied. By means of conditions of power-law expansion and the equation of state of matter less than ?1/3, the relationship among p, w and n, the conditions and the candidate for late-time cosmic accelerated expansion will be discussed in the four classes of f(R) gravity models with non-minimal coupling. Furthermore, in order to keep to considering models that are realistic ones, the Dolgov–Kawasaki instability will be investigated in each of them.