Theoretical Study On The Problems Related To F(R,T) Modified Gravity Model

At the end of the 20th century,the data analysis ofI_a supernova observation,the large-scale structure of the universe and the cosmic microwave background radiation show that our universe is in a state of accelerating expansion.To explain the accelerating expansion of the universe,two theories have been developed based on Einstein's field equations.One is to introduce unknown new matter,with negative pressure acting as a repulsive force,which can cause the universe to expand in a state of accelerated expansion,and we call this new matter dark energy.The other is to modify the field equation,which is called the modified gravity theory,such as Brans-Dicke(BD)theory,f(R)theory,f(R,T)theory and so on.f(R,T)gravity model can realize the unification of matter term and acceleration term without any restriction.In this thesis,the f(R,T)modified gravity theory in the modified gravity model is selected for in-depth study.Firstly,the f(R,T)gravity theory is briefly introduced,and three kinds of f(R,T)modified gravity models are briefly explained.Secondly,the dynamic stability analysis of f(R,T)modified gravity is carried out,and the specific f(R,T)modified gravity model is selected to limit the value range of model parameters through the analysis of dynamic stability and the conditions that cosmological quantities need to meet.Then start with the Raychaudhuri equation,derive four energy conditions,and calculate the specific energy conditions of the modified gravity model,and the weak energy conditions among them limit the parameter range of the f(R,T)modified gravity model.The parameter limits of the f(R,T)modified gravity model are constrained by the energy conditions.Finally,using the scale factor and state parameters,the energy density?is substituted into the cosmological equation of f(R,T)modified gravity model,and the function expression f(T)of the energy momentum tensor T is obtained,and the reconstructions of the two models are discussed.