Cosmological Scaling Solution And Statefinder Diagnose For Dark Energy

With the issue of abundant data from observation, the cosmology has entered a golden era. Especially, the recent measurements of type Ia Supernovae (SNe Ia) are the most direct evidence of the presence of accelerating expansion of the universe, which is also confirmed by the combination of results from the large-scale distribution of galaxies and the most precise data on the cosmic microwave background (CMB) from the Wilkinson Microwave Anisotropy Probe (WMAP). The data from WMAP indicate that the universe is almost spatially flat, i. e.Ω_total=1.02±0.02. Furthermore, the studies on large-scale distribution of the galaxies imply the existence of cold dark matter which occupies about 23% of the total energy of the universe, i. e.Ω_CDM=0.27±0.04. These results strongly imply the existence of a dubbed component with negative pressure, which is named as dark energy, and amounts to about 2/3 of the total energy of the universe (Ω_de=0.67±0.06). Dark energy permeates homogenously in all the universe and pushes the universe accelerating expansion. By far, many models have been presented to explain the accelerating expansion of the universe and dark energy, such as the cosmological constant A, slow rolling scalar fields quintessence, phantom, quintom and coupled models etc.In this thesis, in the framework of the standard FRW cosmological model and the five-dimensional big bounce cosmological model, the accelerated expansion of the universe and the dark energy problem are explored. The dissertation includes five sections and our main contributions are given from Sec. 3 to Sec. 5. In Sec. 1, standard FRW cosmological model and the evidence of existence of dark energy from astronomical observation have been introduced. Meanwhile, several dark energy models are introduced also.In Sec. 2, the five-dimensional big bounce cosmological model is introduced. In this model, the universe is a hypersurface embedded in a Ricci fiat five-dimensional manifold which is empty or vacuum from the higher dimensional view. However, from four-dimensional view, it is full of matter induced from the extra dimension, which is named as induced matter.In Sec. 3, the scaling solution was obtained by the autonomous system in the five-dimensional cosmological model. The analysis of the phase-plane is shown that for this 5D scaling solution the universe expands with the same rate as it does in the 4D FRW models and not relies on which 4D hypersurface the universe is located in the 5D manifold. In Sec. 4, several 4D dark energy models have been diagnosed by statefinder parameter {r, s}. It is supposed that the cosmological constant is the simplest model to explain the presence of the accelerating expansion of the universe. Unfortunately, there exist the fine-tuning and coincidence problems in cosmological constant model. However, many dark energy models have been presented to solve or alleviate the two problems. This thesis diagnoses various dark energy models with statefinder parameter {r, s}. In the 4D FRW cosmological model, the quintessence with tracker potential, the phantom model with V(Φ)= V₀ exp(-λΦ²) and the coupled phantom energy with dark matter have been diagnosed by the statedfinder parameter. It is shown that the region of statefinder parameter, the trajectories of r(s) and r(q) are different between the former two models. Especially in attractor phantom model, attractor solution was studied by both phase-plane analysis and evolving trajectories of r(s) and r(q). In coupled phantom model, the two different scaling solutions have been studied by using statefinder parameter. It is found that the evolving trajectories of these two scaling solutions in the statefinder parameter plane are quite different. Meanwhile, the difference between the scenarios with and without the interaction has been contrasted.In Sec. 5, in the five-dimensional big bounce model, the attractor solutions of quintessence and phantom field have been differentiated by statefinder parameter. It is found that the evolving trajectories of these two attractor solutions in the statefinder parameters plane are quite different, through which the effect on evolving of universe from the parameterλin potential also be studied.