Some Issues On The Generalized Brans-Dicke Theory In The Framework Of Metric-formalism And Palatini Formalism

Since the General Relativity(GR)was proposed by the A.Einstein,the modified gravity theory has always been the hot topic.Modified gravity could solve the theoretical or the experimental questions that existed in the GR.In this thesis,we study one of the modified gravity----the generalized Brans-Dicke(GBD)theory.By choosing the different dynamical variables,modified gravity theory can usually be divided into three formalism: the metric formalism,the Palatini formalism and the metric-affine formalism.Considering that some interesting properties have been found in the GBD theory of metric-formalism(including aspects of the cosmology,the weak-field approximation,etc),in this paper we continue to investigate the GBD theory in the metric-formalism and the Palatini-formalism,respectively.Firstly,we derive the field equations by using the variational approach and obtain the linearized equations by using the weak-field approximation method for the GBD theory of Palatini formalism.We show various properties of the geometrical scalar field in the Palatini-formalism of GBD theory: it is massless and sourcefree,which are different from the results given in the metric-formalism of GBD theory.Considering that the modified gravity theory should owns the viable(post)Newton limit,we investigate the solutions of the linearized field equations for the case of a static-point source,and derive the expression of parameterized post Newton(PPN)parameter.It can be shown that the predicted theoretical value for the PPN parameter in the Palatini formalism of GBD theory could pass through the experimental test.Gravitational-waves(GWs)physics is an important aspect for probing the viable gravitational theory and the astrophysics.People often investigate the polarization of GWs by using the weak-field approximation method and the Newman-Penrose(NP)method,etc.In the chapter 3,we apply the NP method to analyse the polarization modes of GWs in the Palatini-GBD theory.Comparing with the General Relativity,we can see that two extra polarization modes of the GWs can be found in the Palatini-GBD theory: the longitudinal and the breathing modes.In the chapter 4,we apply the dynamical system method to study the GBD theory in the metric-formalism,and analyse the stability of critical points in this theory.