Some Issues In Current Accelerating Universe

Recent observations of type Ia supernovae (SNe Ia) and the Wilkinson Mi-crowave Anisotropy Probe (WMAP) indicate that the expansion of the Universeis accelerating at the present time. But the hot big bang model based on theordinary matter component denotes that the expansion of the universe would bedecelerating, which is not consistent with the observation. In order to explain theexpansion of our Universe, we have to modify it properly. There are two mainlyways to deviate from Einstein's gravity. One of them is to introduce an exoticcomponent with large negative pressure, usually referred to as dark energy, inenergy momentum tensor. This is because, from the data sets of WMAP, theamount of dark energy occupies 73% in cosmic budget. So it is reasonably tobelieve that the accelerating expansion of our universe is due to dark energy. Al-ternative to it, one may consider modified theories of gravity which essentially isto modify the part of geometry in Einstein's equation. f(R) theories of gravity isone of the competitive candidates in it.From above two approaches, we discuss some issues in accelerating cosmologyin this thesis. First of all, we extend the study of the new generalized Chaplygingas (NGCG). Specifically, we not only discuss the change rates of the energydensities and the energy transfer of this model, but also perform the Om diagnosticto di?erentiate theΛCDM model from the NGCG and the generalized Chaplygingas (GCG) models. Furthermore, in order to consider the in?uence of dark energyon the structure formation, we also present the evolution of growth index in thisscenario with interaction.Furthermore, the energy conditions and the Dolgov-Kawasaki criterion inf(R) gravity with arbitrary coupling between matter and geometry are derived,which are quite general and can degenerate to the well-known energy conditionsin GR and f(R) gravity with non-minimal coupling and non-coupling as specialcases. In order to get some insight on the meaning of these energy conditions andthe Dolgov- Kawasaki criterion, we apply them to a class of models in the FRWcosmology and give some corresponding results. Finally, we discuss how to realize late-time cosmic accelerated expansion inf(R) gravity with non-minimal coupling between geometry and matter. Underconditions of power-law expansion and the equation of state of matter less than-1/3, the range of the parameter is concretely constrained and the condition andcandidate for late-time cosmic accelerated expansion are also been obtained.