A Kind Of Cosmic Acceleration Mechanism Depending On Extra Dimension And 6-D RS Model

In this thesis, firstly, we reviewed the history and the progress of the Standard Cosmology, and the motivation why the Randall-Sundrum model was proposed and the development of it. Based on the results of the former exploiters, we made further reaseach on the problem of the acceleration of the universe, and gave propose of us. We researched the scenario of 6-D Randall-Sundrum model, and found some significative results.This thesis comprises two parts, in the first part, in order to deal with the puzzle of the latter-time acceleration of the universe, we find a new mechanism; in the second part, the 6-dimensional Randall-Sundrum model was discussedPart I: We modify the FRW model by making the cosmological scale factor R be a function of the coordinate of the extra dimension x₅ , then, we obtain a kind of 5D-metrics. When x₅ is a function of time, the 5D-metrics reduce to 4D form. The signatures of this 4D-metrics can be changed in the evolvement of the universe. And we show that there exists a duality between the changed 4D-metrics and Lorentzian ones, and the curvatures of the two kinds of metrics are reversed (k→- k). It is this duality that gives us a way to alleviate the problem of later-time accelerated expansion of the universe. We give not only the solutions of Einstein equations of this model but also discussion of the solution in different cases.Part II: Our scenario is a generalization of the two-brane Randall-Sundrum model. In RS's model the warp function only depend on one variable, in our scenario the warp function has two variables, i.e. the two extra dimensions. There are two dramatic discoveries after this generalization. The first one is that the cosmological parameter distributes in the two extra dimensions in a form of a cluster of circles, when there are no branes. These circles are not added by hand but derived from the equations, and the radiuses of these circles are proportional to the reciprocal of the root of the cosmological parameter. The other discovery is that four branes whose tensions have the relationship V₁ = V₃ = -V₂ = -V₄ = 3M⁴ distribute on the circle symmetrically.