Higher Dimensional Cosmological Model And Dark Energy

The recent measurements of type Ia Supernovae (SNe Ia) are the most direct evidence of the presence of accelerated expansion of the universe. It 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 flat, i.e. Ω_total = 1.02±0.02. And, the studies on large-scale distribution of the galaxies imply the existence of cold dark matter which ratio is about Ω_cdm = 0.27 ±0.04. All these results strongly imply the existence of an extra component with negative pressure, which amounts to about 2/3 (Ω_de = 0.67±0.06) and permeates homogenously in all the universe and pushes the universe accelerated expansion. This kind of component is dubbed dark energy. To understand the accelerated expansion of the universe and the dark energy, many models have been presented, such as the cosmological constant A, slow rolling scalar fields quintessence, phantom, quintom etc.In this thesis, under the framework of higher-dimensional cosmological model, the accelerated expansion of the universe and dark energy problem are explored. In this model, the universe is a hypersurface embedded in a Ricci flat five-dimensional manifold which is empty or vacuum from the higher dimensional view. But, from four-dimensional view, it is full of matter induced from the extra dimension, named induced matter.At first, based on a class of five-dimensional Ricci flat exact solution which contains two arbitrary functions μ(t) and v(t) of time t, the bounce singularity contrary to the standard big bang singularity is discussed. It is pointed out that, at the bounce point the three five-dimensional topological invariants and energy density are finite but the pressure undergoes a sudden transition from negative infinity to positive infinity. So, it is a matter singularity not a space-time singularity.To understand the evolution of the universe, two functions μ(t) and v{t) are chosen with the induced matter contains cold dark matter Pcdm, radiation p_r and an "unknown" matter p_x-dubbed x-matter. The evolutions of these three kinds of components are discussed and found that the expansion of the universe is accelerating at present. Moreover, it is also founded that the x-matter has the properties of dark energy with negative EOS and the results are compatible with current observations. Here, it must be pointed out that the choices of the functions are difficult.To overcome the difficulty of choices of these two functions, they are transformed into an new arbitrary function f(z) with respect to the new variable redshift z. Now, in the Friedmann's equations, only one function f(z) appears which is transformed from of μ(t), and v(t) does not appear apparently at the same time. So, the choices become easier than before. To solve the coincidence problem, a stage with almost constant ratio of dimensionless energy densities of cold dark matter and dark energy is required-i.e. the appearance of a scaling stage. So, by using f(z) a hyperbolic-tangent function of z, the scaling solution is obtained.In this model, the relation between quintessence potentials and the particular forms of f(z) is discussed. It is pointed out that the scalar potentials in Quintessence models correspond to particular forms of f(z) in our models. Considered this correspondence, it can be found out the function f(z), which makes the choices easier and have stronger physics foundation. Through the model independent EOS of dark energy w(z) and decelerated factor q(z), the relations between w(z), q(z) and f(z) are built. Then, our models also can be constructed from decelerated factor and give predicts on EOS of dark energy and the evolutions of the universe and compare of these predicts with the observations.In summary, the bounce cosmological models have been studied roughly from two facets: the bounce singularity and dark energy including the reconstructions of these models. Through these studies, it is found that with the induced matter containing cold dark matter, dark energy (or x-matter) the predictions of this model is compatible with the current observations. These results make us believe that the universe may have an eternal time, comes from a bounce with matter creation, decelerated expansion at earlier epoch and accelerated expansion at later times. Of course, this is still a rough scenario needed to be added a lot of works, such as the anisotropy of CMB spectrum, the structure formation, etc. It is expected to consummate the model in the future.