Studies On The Dynamical System And Geometrical Diagnostics For The Generalized Symmetric Teleparallel Theory Of Gravity

For the development of gravity theory and the modern cosmology,general relativity（GR）has always played a crucial role.In view of some problems appeared in GR,many modified theories or extended theories of general relativity have also been proposed.The symmetric teleparallel gravity is an equivalent theory of general relativity,which provides a new geometrical explanation for gravity.In this thesis,we will study the f（Q） modified gravity theory in the framework of generalized symmetric teleparallel gravity.Considering some researches have been done in this theory,e.g.on the fields of astronomical observational constraints and cosmology,we apply the dynamical system method and geometrical diagnosis method to explore the relevant f（Q） theoretical model.In the introduction section and the second chapter of this paper,we mainly introduce the theory of symmetric teleparallel gravity and the basic equations for the extended f（Q） modified gravity theory.We also briefly describe the relevant contents of the wormhole physics under this theory.The third and fourth chapters in this thesis are main work for me during my postgraduate period.In the third chapter,we study the dynamic system for the f（Q） cosmological model.It is found that there are five critical points for the selected f（Q） model.According to the eigenvalues of Jacobin matrix,we observe that the system has a stable critical point in the period for the universe dominated by geometric dark energy.In the fourth part,we apply the geometrical diagnosis method distinguish the four f（Q） models in the framework of symmetry teleparallel gravity.According to the calculation results,the evolutions of the four cosmological models in the future are similar to the cosmological constant model.And the r-s pictures are all located in the Quintessence region（r<1,s>0）.Finally,we analyze the influence of different power-law functions and different values of model parameters on diagnosis behavior.It is shown that the shape of r-s images for the model with different power-law functions(such as （-Q）^1?2 and （-Q）²)are significantly different;But the change of the value for model parameter（related to the power-law function）has little effect on the r-s diagnostic image.Only correction from the constant term is introduced,the change of the model parameter value has more obvious effect on the pictures of geometric diagnostic.