在此篇論文中，我們將從纖維叢理論至黎曼—卡當時空理論完整介紹龐加萊規範重力理論。次外，我們將從龐加萊規範重力理論出發延伸出多種不同重力理論。特別是一種純量撓場重力在宇宙學中的效應及其研究。在該理論中，我們將純量撓場產生的幾何效應等效地視為暗能量並研究其狀態方程式之演化。此理論中存在兩種特殊解，分別是常曲率解及正能量解。在前者中，我們發現純量撓場的狀態方程式在宇宙的不同階段會對應不同的定值。舉例而言，在相對論性物質主導的時期會對應 w=1/3，在非相對論性物質主導時期則對應w=0。然而在宇宙晚期純量撓場可以造成宇宙加速膨脹，因而可被視為暗物質的候選理論之一。在後者正能量解中，該曲率通常不會維持定值以致需要使用數值解。使用數值方法，我們發現一種現象是在早期宇宙時狀態方程式通常會有漸進行為，而在低紅移時期則會跨越幽靈場極限。藉由進一步的勞倫級數解析我們發現，撓場密度函數會趨近於相對論性物質的密度函數，也就是O(a-4) ，其中a(t)是宇宙標度因子，並且壓力函數會有穩定點。壓力與密度的比例在高紅位移處會趨近1/3。使現象在以往相關的文獻中並未被提及。我們另外展示出數值的圖示。我們另外用外微分形式建構出平移重力的額外高維理論。我們另外特別藉由選取不同型態時空上的纖維而探討卡魯扎-克萊因理論及高維投影出的膜世界情景。另外，我們發現在平移高維膜理論重力下的弗里德曼-勒梅特-羅伯遜-沃爾克宇宙與愛因斯坦高維膜理論重力的弗里德曼-勒梅特-羅伯遜-沃爾克宇宙有相同的場方程解。因此，兩者擁有共同的宇宙演化，也就是依循相同的弗里德曼方程。

We give a complete formulation of Poincare gauge theory, starting from the
bre bundle formulation to the resultant Riemann-Cartan spacetime. We also
introduce several diverse gravity theories descendent from the Poincare gauge
theory. Especially, the cosmological eect of the simple scalar-torsion (0+) mode in
Poincare gauge theory of gravity is studied. In the theory, we treat the geometric
eect of torsion as an eective quantity, which behaves like dark energy, and study
the eective equation of state (EoS) of the model.
We concentrate on the two cases of the constant curvature solution and positive
kinetic energy. In the former, we nd that the torsion EoS has dierent values
corresponding to the stages of the universe. For example, it behaves like the
radiation (matter) EoS of wr = 1=3 (wm = 0) in the radiation (matter) dominant
epoch, while in the late time the torsion density is supportive for the accelerating
universe. In the latter case of positive kinetic energy, we nd the (ane) curvature
is not constant in general and hence requires numerical solution. Our numerical
analysis shows that the EoS in general has an asymptotic behavior in the high
redshift regime, while it could cross the phantom divide line in the low redshift
regime. By further analysis of the Laurent series expansion, we nd that the
early evolution of the torsion density T has a radiation-like asymptotic behavior
of O(a􀀀4) where a(t) denotes the scale factor, along with a stable point of the
torsion pressure (PT ) and a density ratio PT =T ! 1=3 in the high redshift regime
(z  0), this is dierent from the previous result in the literature. Some numerical
illustrations are also demonstrated.
We construct the extra dimension theory of teleparallel gravity by using dierential
forms. In particular, we discuss the Kaluza-Klein and braneworld scenarios
by direct dimensional reduction and specifying the shape of the bre. The FLRW cosmological scenario of the braneworld theory in teleparallel gravity demonstrates
its equivalence to general relativity (GR) in the eld equations, namely they possess
the same Friedmann equation.

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