Geometric Diagnostics For F(R) Modified Gravitational Theory With The Palatini Formalism

Both the accelerating universe and modified gravitational theories are hot regions for studying on gravity physics.In this thesis,we investigate the accelerating universe with the framework of Palatini-f(R)theory.The first section of our thesis is the introduction.In this section we briefly introduce the discovery of accelerating universe and two explanations for this accelerating expansion.In addition,we elaborate two variational methods that exist in modified gravitational theory and the geometric diagnostic methods in cosmology.Given that geometric diagnostic methods have been widely applied to the accelerating cosmology with the framework of metric-formalism modified theory,in the section chapter we focus on introducing four popular modified gravity theories(i.e.f(T),f(Q),f(R,T)and f(Q,T)theory)in the metric formalism and their geometric diagnosis.Lots of f(R)models have been constructed to interpret the accelerating expansion of universe.One can distinguish these models by using the geometrical diagnostic method.In chapter 3 of this thesis,we explore the behaviors for four f(R)models(the popular Starobinsky model,Hu-Sawicki model,Type Ⅱ ΛCDM-like f(R)model and Type ⅢΛCDM-like f(R)model)by using the geometric diagnostic method.It is well known that a large number of models in the metric-formalism gravitational theories have been distinguished according to the geometric diagnostic method,but it is rare to explore the geometric behaviors in the Palatini formalism of modified theory.In this thesis,we mainly use this method to identify the f(R)modified gravitational models in the Palatini formalism.According to the geometrical diagnostic pictures,we can see the differences between above models and their deviations from the standard cosmological constant model.Also,it is easy to observe that the(r,s)values in the Hu-Sawicki model more approach to those in the ΛCDM model at the current period,i.e.relative to the ΛCDM model,Hu-Sawicki model has a smaller deviation than other three models,while the Type Ⅲ ΛCDM-like f(R)exponential model has a larger deviation.In addition,the evolutional behaviors of deceleration parameter q in the four f(R)models are similar to those in ΛCDM model,while the trajectories of r for all models are obviously different,which indicate that the geometrical parameter r can be applied to distinguish different cosmological models easily.Finally,comparing with other three viable models it is found that the behavior of Hu-Sawicki model approach to ΛCDM model more easier,and it has the smallest value of r in the early universe.It indicates that the behavior for this model is different from that for other three models at earlier universe.