F(R, L_m) Gravity And The Researches Of Relevant Problems

Recently, a number of the observations indicate that the expansion of the Universe is ac-celerating at the present time, rather than slowing down, which is not consistent with the de-celerating expansion of the Universe in standard cosmological. In order to explain the truth,one propose many correction ways, either introduce dark energy in the right side of Einsteinfield equations, or modify the component of geometry in Einstein’s equation, namely the theoryof modified gravity. Two theories all can explain the accelerating expansion of the Universe,but because the nature of dark energy is unknown, modified gravity is extensively investigatedlately, and f (R) gravity is the representative one in it. By varying the action, the field equationsare obtained in f (R) gravity as before. However, not all of the models are viable. In recentyears, one can constrict the models by energy conditions and stability.First of all, the basic knowledge of f (R, L_m) gravity is introduced in this paper, thenunder the condition of a power-law expansion, the cosmological models which accord with thecurrent astronomical observations are derived by using the field equations limit the parametersof a kind of f (R, L_m) gravity models, the behavior of which imitates the effective quintessencedark energy or the effective phantom dark energy. Moreover, due to keep the requirementthat gravity is attractive and so on, we constrain the f (R, L_m) gravity by applying the energyconditions (namely the strong energy condition,the null energy condition, the dominate energycondition and the weak energy condition). By Raychaudhuri equation, the energy conditionsin f (R, L_m) gravity are obtained, which can return to the energy conditions in f (R) gravity withcoupling and General Relativity, so this model is more general. In order to further understandthe meaning of the energy conditions, we apply them to restrict the parameters of the concretef (R, L_m) gravity models, and the possible values of the parameters are obtained. Finally, inorder to be viable, the theory of modified gravity must be free of short time scale instabilities. Bytaking trace to the field equations and expanding the space-time quantities of interest as the sumof a background with the constant curvature and a small perturbation, the Dolgov Kawasakicriterion in f (R, L_m) gravity is derived, which also can return to the Dolgov Kawasakicriterion in f (R) gravity with non-minimal and arbitrary geometry-matter coupling. It’s worthnoting that the DK criterion is related to the terms of the coupling between matter and geometry,and is unrelated to the pure terms of the matter or the pure terms of the geometry. We discussthe stability of our models by using the DK criterion.