Study On The Related Problems Of Accelerated Expansion Of The Universe

At the beginning of the 20th century,Einstein released his general relativity(GR),and at-tempted to generalize the whole universe's evolutionary rule according to the gravitational field equation and the cosmological principle.The first cosmological model he proposed believes our universe should be finite and static,this went against the fact that the "redshift" of galaxy spectra observed by Hubble.The concept of the expansion of our universe was gradually es-tablished over with time.Present cosmological observations point to a cross-checked message that our universe is undergoing an accelerating expansion.Scientists have made two changes to the Einstein field equation in order to explain the accelerating expansion of the universe.One is an extra component with negative pressure namely dark energy has been proposed,although scientists do not know the origin and distribution of dark energy has been proposed,but it has the power of promoting the accelerated expansion of the universe.The other is to modify the spacetime geometry of the universe,that means there will be a new theory of gravity without the need for dark energy to explain the expansion of the universe.In this thesis,we learn some relevant issues of the universe's accelerating expansion under the FRW metric.In the first part,two theoretical explanations of the accelerating expansion of the universe are described,and introduced some usual dark energy models and the modified gravity models.Then we,studied the modified Chaplygingas(MCG)model.The MCG model is a generalized form of CG model and it also can be used as a unified model of Dark Matter(DM)and Dark Energy(DE).The evolution of the cosmological quantities of the model,the linear perturbation trajectory of the growth variable T and the growth index f with the scale factor a(t)are analyzed and discussed in detail.We use state finder and Orn diagnostic to compare and distinguish the MCG model with other different dark energy models,and the dynamical stability analysis of the model is given,and we found an attractor in the MCG model with interaction,it shows that the stable point has the properties of the cosmological constant,which is a good explanation for the acceleration of the universe at this time.Finally,we give the action,field equation and energy conditions of the f(R)modified gravity model,through the energy conditions,two kinds of feasible f(R)models' parameters are constrained,and the range of the free parameters is presented.