Studies On The Weak Field Approximation Of Generalized Brans-Dicke Theory

General relativity(GR)plays an important role in the development of gravitational theory.GR established by the Einstein broke the conventional expressional way of the classical gravity theory.Although GR was questioned by some researchers at the beginning,the several experiments in the solar system strongly supported this theory.However,there are some problems in the GR theory,which are hard to interpret in theory and experiments.So,the modified gravity theories are always investigated and studied by researchers.There are plenty of the modified gravity theories.The f(R)theory and the Brans-Dicke(BD)theory are two simple modified gravity theories.In this paper,we firstly describe the f(R)theory.In the f(R)theory,we introduce the gravitational field equation,the scalar tensor representation,the local gravitational test,and the chameleon mechanism.Secondly,we briefly state the BD theory,and two extended BD theories:the BDA theory and the BDV theory.Finally,we study the generalized BD(abbreviated as GBD)theory.The GBD theory is obtained by generalizing the Ricci scalar R to an arbitrary function f(R)in the action of the original BD theory.Comparing with other theories,some interesting properties have been found or some problems existing in other theories could be solved in the GBD theory.For example,(1)the state parameter of geometrical dark energy in the GBD model can cross over the phantom boundary w ?-1,without bearing the problems existing in the quintom model(e.g.the problem of negative kinetic term and the fine-tuning problem,etc);(2)f(R)theory is equivalent to the BD theory with a potential(BDV)with the couple parameter?BD=0,where the kinetic term of field in the equivalent BDV theory is absent.While the scalar fields in the GBD own the non-disappeared kinetic term,when one compares the GBD theory with the f(R)theory.In this thesis,using the method of the weak-field approximation,we derive to obtain the linearized gravitational field equation and the scalar field equation in the GBD theory.The linearized equations of the gravitational field and the BD scalar field are given.We investigate the solutions of the linearized field equations in the GBD theory for a point mass.It is shown that the problem of the/value in the f(R)theories can be solved in the GBD theory.In addition,we explore the gravitational radiation in the vacuum for the GBD theory.It is found that the gravitational radiation in the GBD theory has new freedoms beyond the two standard modes in the general relativity theory.