The Consistency Conditions And Constraints On Generalized F(R) Gravity With Arbitrary Matter-gravity Coupling

Recent astrophysical observations have indicated that the expansion of our Universe is accelerating at the present time.In principle,this phenomenon can be explained by either dark energy or modified theories of gravity.f(R) gravity is one of the competitive candidates in modified theories of gravity.And the conditions of viable cosmological models have been derived.In this thesis,we first introduce the background knowledge of modern cosmology.Sec-ondly,we introduced the development of the modified theories of gravity briefly,and expounds the generalized f(R) with arbitrary matter-gravity coupling emphatically.Finally,we study the consistency conditions of the generalized f(R) gravity by extending f(R) gravity with non-minimal coupling to the generalized f(R) with arbitrary matter-gravity coupling.Concretely,we discuss the three particular models of generalized f(R) by means of consistency conditions,and find that the second model is not physically viable so as to be ruled out.Moreover,we further constrain on the first model and the third model by using the Dolgov-Kawasaki(DK)stability criterion,and give the value ranges of the parameters in the first model and the third model.It is worth stressing that our results include ones in f(R)gravity with non-minimal coupling as special case of Q(L_m)= L_m.