The Theoretical Study On The Stability And Polarization Modes Of Gravitational Wave For F(R) Modified Gravity Model

A large number of astronomical observations(such as type Ia supernovae,cosmic mi-crowave background anisotropy and baryon acoustic oscillations in large scale structures)in-dicate that the expansion of the universe is accelerating.To explain this phenomenon,various theories represented by the dark energy theories and the modified gravity theories have been proposed,in which f(R)modified gravity theory is one of the most competitive gravity theories.The function f(R)generalizes the Einstein-Hilbert Lagrangian by adding corrections that are non-linear functions of the curvature.Due to the diversity of the form of f(R),many models in f(R)modified gravity theory have been proposed,such as Starobisky model.Hu-Sawicki model and Tsujikawa model et la.In this thesis,firstly,applying the dynamic stability analysis of autonomous system,Dolgov-Kawasaki instability criterion and four energy conditions in f(R)modified gravity theory to a class of f(R)specific model f(R)=Re-(?2/R)?,not only a stable point of this dynamic au-tonomous system is obtained under the condition of 3/1<?<2,but also the restricted condition of 0<??1 is given for the model parameter ?.Then,the polarization modes of gravitational waves in f(R)modified gravity is studied,which is a hot topic at the forefront.The Newman-Penrose quantities which can represent the polarization modes of gravitational waves is applied to this specific model of f(R)modified gravity.It can be seen that there are three non-zero quantities?2,?22 and?4 in this model.?2 corresponds to longitudinal scalar mode;?22 cor-responds to breathing scalar mode;?4 is complex and represents+and × tensorial polarization modes.So,there are two additional scalar modes besides the usual two tensor modes presented in General Relativity in this model.Finally,in order to better understand the scalar degrees of freedom of the model,we study the properties of the potential energy and mass of the scalar field in the Jordan and Einstein frames.